How do you differentiate #f(x)=(x^3-2x+3)^(3/2)# using the chain rule? How do you differentiate #f(x)=sqrt((1-xe^(2x))^3# using the chain rule.? How do you differentiate # y =x sqrt((4-x^2) # using the chain rule? Differentiate with respect to x #e^tanx/x^(1/2)# ? ... BODMAS Rule. How do you differentiate # f(x)=cos(e^((lnx-2)^2 ))# using the chain rule.? If #f(x)= tan5 x # and #g(x) = -x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? {\displaystyle '=\cdot g'.} How do you use the chain rule to differentiate #y=1/(t^2+3x-1)#? Brush up on your knowledge of composite functions, and learn how to apply the chain rule correctly. How do you use the chain rule to differentiate #y=root5(x^2-3)/(-x-5)#? How do you find the derivative of #y=sqrt(x)/(1+sqrt(x))#? How do you use the chain rule to differentiate #f(x)=sqrt(4x^3+6x)#? How do you find the derivative of # ln(x+1)#? Let's see what that looks like mathematically: Let's say we have the composite function #sin(5x)#. How do you find the derivative of #f(x)=x^2-(1/x)#? A technique that is sometimes suggested for differentiating composite functions is to work from the “outside to the inside” functions to establish a sequence for each of the derivatives that must be taken. How do you differentiate #f(x) = sec(tan(sec(tan(x))))#? How do you differentiate #f(x)=1/lnsqrt(-e^(4x)-2)# using the chain rule.? If #f(x) =sec^2(x/2) # and #g(x) = sqrt(5x-1 #, what is #f'(g(x)) #? How do you find the derivative of #sqrt(x+7)#? 2) Use the chain rule and the power rule after the following transformations. How do you find the derivative for #1/sqrt(1-x^2)#? What is the derivative of #g(x)= x^2*sqrt(1-x^2)#? Let us find the derivative of . How do you find the derivative of #(1-y^2)^(1/2)#? How do you differentiate #sqrt(1+(1/x))#? How do you find the derivative of #y=2(5x+3)^7-1# using the chain rule? How do you differentiate # f(x)= (xe^x+x)^2 # using the chain rule.? How do you differentiate #f(x)=sqrt((3x^2)/(2x-3)) # using the chain rule? How do you find the derivative of #C=7/4x+8x²#? How do you differentiate #f(x) = sin(xcos(x))# using the chain rule? What is the derivative of #sqrt(x^2-1) / (x^2+1)#? In applying the Chain Rule, think of the opposite function f °g as having an inside and an outside part: General Power Rule a special case of the Chain Rule. The chain rule is used when you want to differentiate a function to the power of a number. That is, if f and g are differentiable functions, then the chain rule expresses the derivative of their composite f ∘ g — the function which maps x to f {\displaystyle f} — in terms of the derivatives of f and g and the product of functions as follows: ′ = ⋅ g ′. How do you differentiate #f(x)=sec(1/sqrt(3x^2-4) ) # using the chain rule? To see the proof of the Chain Rule see the Proof of Various Derivative Formulas section of the Extras chapter. How do you find the derivative of #e^((x^2)/2)#? How do you differentiate #f(x)=sqrt(e^(cot(1/x)# using the chain rule.? If #f(x) =-sqrt(3x-1) # and #g(x) = (2-1/x)^2 #, what is #f'(g(x)) #? What is the derivative of # sin^2(x) cos (x)#? How do you differentiate #f(x)=tan(1-3x) # using the chain rule? If #f(x) =-e^(2x-1) # and #g(x) = -3sec^2x^2 #, what is #f'(g(x)) #? If #f(x) =xe^(2x-3) # and #g(x) = sin3x #, what is #f'(g(x)) #? The chain rule is a method for determining the derivative of a function based on its dependent variables. How do you differentiate #f(x) = (1-3sqrt(2x^2-1))^2 # using the chain rule? How do you find the derivative of #e^sqrt(x)#? How do you differentiate # f(x)=sin(e^((lnx-2)^2 ))# using the chain rule.? How do you find the derivative of # cos(1-2x)^2#? What is the derivative of #(3+2x)^(1/2)#? Suppose that f(2) = −3, g(2) = 5, f '(2) = −2, and g'(2) = 4. How do you find the derivative of # sin^2(x/6)#? How do you differentiate #f(x)=cos(sqrt(3+e^(x^2)))# using the chain rule? How do you use the chain rule to differentiate #y=2(x^3-x)^-2#? This rule allows us to differentiate a vast range of functions. How do you differentiate #f(x)=(sin(tanx))^3#? How do you differentiate #f(x)=sqrt(1-e^(4x))# using the chain rule.? (x+1) but it will take longer, and also realise that when you use the product rule this time, the two functions are 'similiar'. How do you differentiate #y= ln e^(6x+1)#? How do you differentiate # y=sec (3x^2 - x)# using the chain rule? $$f(x) = \blue{e^{-x^2}}\red{\sin(x^3)}$$ Step 2. If #f(x) =-e^(2x-1) # and #g(x) = 5sin^2x^2 #, what is #f'(g(x)) #? How do you differentiate #tan(2pix+pi/2)#? How do you differentiate # f(x)=e^sqrt(3lnx+x^2)# using the chain rule.? What is the derivative of #y= ln(1 + e^(2x))#? How do you differentiate #f(x)=x/ln(sqrt(1/x))# using the chain rule? How do I solve this derivative at one point? How do you differentiate #f(x)=sqrt(cose^(4x)# using the chain rule.? How do you differentiate #f(x)=x/arcsinsqrt(ln(1/x^2)# using the chain rule? How do you find the second derivative of #y=x^5#? Let f be a function of g, which in turn is a function of x, so that we have f(g(x)). How do you differentiate # f(x)=e^(((ln(x^2+3))^2)# using the chain rule.? How do you find the derivative of #f(x)=(8x+3)^.5#? Step 1. How do you differentiate # F(x) = 3x^2 + 12#? How do you find the derivative of # f(t)=sin^2[e^(sin^2)t]# using the chain rule? How do you find the derivative of #y= x/sqrt(x^2+1)# ? How do you use the chain rule to differentiate #y=(-3x^5+1)^3#? How do you differentiate #y = e^(-2x + x^2)#? What is the derivative of #ln[(x(x^2+1)^2)/(2x^3-1)^(1/2)] #? How do you calculate the derivative of #y=sqrt(4x^3)#? How do you use the chain rule to differentiate #y=2(x+3)^(1/2)#? We will have the ratio Section 2-6 : Chain Rule. How do you use the chain rule to differentiate #y=sqrt(x^2-7x)#? How do you use the chain rule to differentiate #y=(x+1)^3#? How do you differentiate #f(x)=sin^2(sqrt(3x/(x-1)^2))*cos2x # using the chain rule? How do you find the derivative of #3arccos(x/2) #? The following three problems require a more formal use of the chain rule. WORKSHEETS. How do you use the chain rule to differentiate #y=-2csc^6x#? How do you differentiate #f(x) = sqrt(arctan(2x^3) # using the chain rule? To avoid confusion, we ignore most of the subscripts here. How do you find the derivative of #(x^2 + 1/x)^5#? Identify the factors in the function. How do you find the derivative of #(x^2+x)^2#? How do you differentiate #f(x)=(cos^2x^2)^(7/3)# using the chain rule? If #f(x)= 3x^3-2 # and #g(x) = e^x #, what is #f'(g(x)) #? If #f(x)= cos 4 x # and #g(x) = 2 x #, how do you differentiate #f(g(x)) # using the chain rule? What is the derivative of #sqrt(x+13) / ((x-4)(root3(2x+1))#? Can you explain how the chain rule work in real life? How do you find the derivative of #sqrt(e^(2x) +e^(-2x))#? How do you use the chain rule to differentiate #y=(x^4+3x)^-2#? How do you differentiate #y=e^(-5x)cos3x#? How do you use the chain rule to differentiate #y=(x+1)^(-1/2)#? How do you find the derivative of #2sec((3x+1)^(1/2))#? What is the derivative for #f(x)=sqrt(x^2-1)#? How do you differentiate #f(x)=cos(x^3)#? How do you differentiate #f(x)=(x^3-5x)^4#? How do you differentiate #ln[(x^4-3x^3+1)^(1/2)] #? How do you differentiate # f(x)= (xe^x+4)^3 # using the chain rule.? What is Derivative Using Chain Rule. How do you differentiate #f(x)=e^(4^(1/(x^2)))# using the chain rule? How do you differentiate #f(x)= 2 / (e^x + e^-x)^3#? How do you differentiate # f(x)=e^sqrt(1/x^2)# using the chain rule.? How do you differentiate #f(x) = sqrt(arctan(e^(x-1)) # using the chain rule? How do you differentiate #y=sqrt(2-e^x)#? How do you use the chain rule to differentiate #y=(x^2+5x)^2+2(x^3-5x)^3#? How do you find the derivative of # ln(x^3)#? How do you differentiate # f(x)=1/sqrt((7-2x^3)# using the chain rule.? How do you differentiate #f(x)=tan(sqrt(x^2-3)) # using the chain rule? How do you differentiate #f(x)=sec(1/sqrt(3x) ) # using the chain rule? What is the derivative of #sqrt(x^2-2x+1)#? How do you find the derivative of #f(x)= [(2x-5)^5]/[(x^2 +2)^2]# using the chain rule? How do you use the chain rule to differentiate #y=((x+2)/(x+1))^3#? How do you differentiate #f(x)=e^(sin(2/x)# using the chain rule.? bookmarked pages associated with this title. How do you use the chain rule to differentiate #y=(2x-1)^4/(x+1)^2#? How do you find the derivative for #k(x) = sin (x^2+2)#? Even though we had to evaluate f′ at g(x)=−2x+5, that didn't make a difference since f′=6 not matter what its input is. What is the derivative of #(sqrtx-1)/sqrtx#? How do you differentiate #f(x)=sec(1/e^(x-4) ) # using the chain rule? What is the derivative of #f(x) = x^(5/2) #? What is the derivative of # y = x [sec (3 - 8x)]#? If #f(x) =x-xe^(2x+4) # and #g(x) = cos9x #, what is #f'(g(x)) #? How do you differentiate #g(t)=1/(t^4+1)^3#? How do you differentiate #f(x)=4x ln(3sin^2x^2 + 2)# using the chain rule? How do you solve the derivative of #sin^2x# ? How do you differentiate #f(x)=ln(sin(e^{x}))#? How do you find the derivative of #y=sqrt(1+2x)#? How do you differentiate #f(x)=csce^(4x)# using the chain rule.? How do you use the chain rule to differentiate #y=(x^2+3x)^(-1/2)#? How do you find the derivative of #xsqrt (1-x)#? How do you differentiate #f(x)=(ln(sinx)^2-3xln(sinx)+x^2ln(cos^2x^2)# using the chain rule? How do you find the derivative of #w=(1+4x^3)^-2#? Find second derivative of #y# if #x^6+y^6=1#? How do you use the chain rule to differentiate #y=(5x^4+1)^2#? How do you find the derivative of #y= 10^(1-x^2)# ? How do you find the derivative of #f(x)=2/(6x+5x+1)^2#? How do you determine #(dy)/(dx)# given #y=cos(1-x)#? How do you differentiate #f(x)=cos(tanx)# using the chain rule? It is the counterpart to the chain rule for differentiation, in fact, it can loosely be thought of as using the chain rule "backwards". How do you differentiate #f(x) = (2x+1)^7# using the chain rule? What is the derivative of #y = sin(tan(5x))#? How do you use the chain rule to differentiate #y=-5/(3x^2-4)^6#? How do you find the derivative of #r= 2theta sqrt(sec theta)# using the chain rule? Eg: (26x^2 - 4x +6) ^4 * Product rule is used when there are TWO FUNCTIONS . How do you use the chain rule to differentiate #y=sin^2x/cosx#? How do you find the derivative of #y= sin{cos^2(tanx)}#? How do you use the chain rule to differentiate #y=sin4x^3#? How do you differentiate #f(x)=cot(1/sqrt(x)) # using the chain rule? If #f(x)= sqrt(x-2 # and #g(x) = e^(2x #, what is #f'(g(x)) #? Find the first and second derivative of #(2lnx)/x#? If #f(x)= x^2-x # and #g(x) = x^( 1/3 ) #, what is #f'(g(x)) #? How do you differentiate #f(x)=-sinsqrt(1/(x^2))# using the chain rule? How do you find the derivative of #sqrt x^2#? How do you use the chain rule to differentiate #y=e^(sinx)#? What is the derivative of # ( cos (pi*x) +1 ) / x#? All functions are functions of real numbers that return real values. How do you find the derivative of #sqrtθ sin θ#? Interpretation 1: Convert the rates. How do you differentiate #f(x)=(4x-x^2)^(1/2)/x^2# using the chain rule? How do you differentiate #f(x)=sqrt(csc(2/x ) # using the chain rule? Click HERE to return to the list of problems. How do you find the derivative of #y=ln(e^x+3)# ? How do you differentiate #3sin^2(3x) # using the chain rule? How do you differentiate # y =cos(3sqrtx+7) # using the chain rule? How do you use the chain rule to differentiate #root9(-cosx)#? How do you find the derivative of #(1+x)^(1/x)#? How do you differentiate #f(x)=cot(e^sqrt(x^2-1)) # using the chain rule? If #f(x) =csc^3(x/4) # and #g(x) = sqrt(x^3+3 #, what is #f'(g(x)) #? How do you use the chain rule to differentiate #y=(4x^5-1)root3(x+1)#? How do you differentiate #f(x)=e^(secsqrtx)# using the chain rule.? What is the derivative of #cos^4(x)-sin^4(x)#? $\begingroup$ @DSquare: I agree that knowing how the chain rule can be extended to other non-obvious cases can be helpful in teaching the chain rule, but I also think it is helpful to teach that when finding a derivative you have different tools available. How do you find the derivative of #ln(x^2+1)#? How do you differentiate #f(t)=1/(t^(-1/2))# using the chain rule? How do you use the chain rule to differentiate #y = e^lnx#? How do you differentiate #f(x)=sqrt(((3x)/(2x-3))# using the chain rule? How do you differentiate #y = ln(x^(1/2))#? How do you differentiate #f(x) = (4x^3 + 2x) ^ - 4#? How do you use the chain rule to differentiate #y=((x+1)/(x-2))^5#? What is the derivative of # cos(pi*t/6)#? How do you differentiate #f(x)=x * (4-x^2)^(1/2)# using the chain rule? Use the Chain Rule to find the derivative of the function. How do you use the chain rule to differentiate #log_13(8x^3+8)#? What is the derivative of #ln(sqrt(sin(2x)))#? How do you differentiate #sqrt(sin^3(1/x^2) # using the chain rule? The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. What is the derivative of # f(x)= x^(4/5) (x-5)^2#? What is the derivative of #cos(a^3+x^3)#? How do you differentiate #f(x) = ln(sqrt(arcsin(e^(3x)) ) # using the chain rule? In this example, we use the Product Rule before using the Chain Rule. How do you use the chain rule to differentiate #1/-sinx#? How do you differentiate given #y = (sec)^2 x + (tan)^2 x#? How do you use the chain rule to differentiate #f(x)=sin(cos(tan(x^3+sin(x^2))))#? What is the derivative of #f(x)=(pi/x^5)(1/(e^(1/x)-1))#? How do you find the derivative of #y= x*sin(1/x)# ? The composition of two functions $f$ with $g$ is denoted $f\circ g$ and it's defined by [math](f\circ g)(x)=f(g(x)). How do you differentiate #f(x)=sqrtcos(e^(4x))# using the chain rule.? How do you differentiate given #f (x) = 3 arcsin (x^4)#? Most problems are average. How do you find the derivative of #3e^ (-3/x)#? How do you find the fourth derivative of #e^(2x)#? Before we discuss the Chain Rule formula, let us give another example. How do you differentiate #f(x)=cot(sqrt(x^2-1)) # using the chain rule? How do you use the chain rule to differentiate #y=tan(x^2)+tan^2x#? Alternatively, by letting h = f ∘ g, one can also … The chain rule can be used to differentiate many functions that have a number raised to a power. How do you differentiate # f(x)=e^((lnx-2)^2 # using the chain rule.? h(x) = g(x) / 1 + f(x), Differentiate the function? How do you find the derivative of #y = x^(cos x)#? How do you differentiate #f(x)=(x^2+1)^3# using the chain rule? How do you find the derivative of #lnsqrt x#? Just use the rule for the derivative of sine, not touching the inside stuff (x 2), and then multiply your result by the derivative of x 2. How do you differentiate # y =-2e^(xcosx)# using the chain rule? If #f(x)= cot5 x # and #g(x) = 2x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? How do you use the chain rule to differentiate #r=sec2thetatan2theta#? If #f(x)= (5x -1)^3 # and #g(x) = 3x^( 2/3 ) #, what is #f'(g(x)) #? How do you find the derivative of #2cos^2(x)#? How do you use the chain rule to differentiate #y=(x^2+3)^4#? How do you differentiate # y =(3x-2)^10 # using the chain rule? What is the derivative of #sqrt(x - 1)/sqrtx#? How do you use the chain rule to differentiate #y=(3x^2+1)^4#? If #f(x)= - e^x # and #g(x) = 5 x #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate # 3/4 * (2x^3 + 3x)^(-1/4)#? How do you use the chain rule to differentiate #y=(4x^3-7)^4(3x+2)^10#? Example of Chain Rule. If #f(x) =-e^(x) # and #g(x) = 3csc^2x^2 #, what is #f'(g(x)) #? Is there a chain rule for partial derivatives? How do you differentiate #f(x)=e^(cscsqrtx)# using the chain rule.? How do you differentiate # f(x)=e^sqrt(1/x^2-x)# using the chain rule.? In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x) . How do you differentiate #f(x)=cos(sqrt((cosx^2))) # using the chain rule? What is the derivative of #f(x) = sec(5x)#? Removing #book# How do you differentiate #sqrt(2x) - x^3 #? What is the derivative of #sin^2 x + cos^2 x#? To illustrate this, if we were asked to differentiate the function: The chain rule is used to differentiate composite functions. How do you differentiate # y =sin(ln(cos x)) # using the chain rule? If z is a function of y and y is a function of x, then the derivative of z with respect to x can be written \frac{dz}{dx} = \frac{dz}{dy}\frac{dy}{dx}. What is the first differential of #y = t^(3/2)(16-sqrtt)#? For example, if a composite function f( x) is defined as WHEN TO USE CHAIN RULE. Let's see what that looks like mathematically: Chain Rule: #f'(g(x))*g'(x)# How do you find the derivative of #cos(pi/2)#? How do you differentiate #f(x)=x(1+e^(x^2))^(1/5)# using the chain rule? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you differentiate #y=(4/ln2)(x^(lnx))(lnx+2ln(cosx))#? How do you differentiate # y =2x^3(x^3 - 3)^4 # using the chain rule? How do you use the chain rule to differentiate #y=(x+1)^(1/2)#? How do you differentiate #3sin^3(2x^2) # using the chain rule? How do you differentiate # y =(−7 x^2 − 5)^8 # using the chain rule? How do you differentiate #f(x)=sec(8x ) # using the chain rule? How do you use the chain rule to differentiate #y=(-x^4-3)^-2#? © 2020 Houghton Mifflin Harcourt. How do you find the derivative of #cos(pi*x^2)#? How do you differentiate #f(x) = (x+sqrtx)^(3/2) # using the chain rule? Note that because two functions, g and h, make up the composite function f, you have to consider the derivatives g′ and h′ in differentiating f( x). How do you differentiate #f(x)=(cos x+ 4sin^2x^2)^6# using the chain rule? How do you differentiate #f(x)=sqrtsin(1/lnx^2)# using the chain rule? How do you differentiate #f(x)=e^(5x^2+x+3) # using the chain rule? How do you differentiate #f(x)=1/cossqrt(lnx)# using the chain rule? And, sure enough, the hard thing can be to choose the right tool. How do you differentiate #f(x) = sin(sqrt(arccosx^2)) # using the chain rule? How do you differentiate # f(x)=ln(x^2-x)# using the chain rule.? If #f(x)= 1/x # and #g(x) = 1/x #, how do you differentiate #f'(g(x)) # using the chain rule? Example 1 Use the Chain Rule to differentiate R(z) = √5z − 8. If #h(x)=sqrt(4+3f(x))# where f(1)=7 and f'(1)=4, how do you find h'(1)? How do you find the derivative of #y=x*sqrt(16-x^2)#? What is the second derivative of # (x^2-1)^3#? Let f(x)=6x+3 and g(x)=−2x+5. How do you differentiate #f(x)=sqrt(e^(5x^2+x+3) # using the chain rule? How do you find the derivative of #f(x)=(6x-2)^2#? How do you differentiate #f(x) = ln(sqrt(arcsin(e^(2-x^2)) ) # using the chain rule? How do you find the derivative of #sqrt(x^2-1) / (x^2+1)#? How do you find the derivative of #x*(sqrt(4-x^2))#? How do you use the chain rule to differentiate #y=sec2x^4#? How do you differentiate # f(x)= (6e^(-x)+2)^3 # using the chain rule? Now, for the first of these we need to apply the product rule first: To find the derivative inside the parenthesis we need to apply the chain rule. Indeed, we have So we will use the product formula to get How do you find the derivative of # y = sin(x cos x)# using the chain rule? How do you find the derivative of #y= sqrt((x-1)/(x+1))# ? How do you differentiate # y =(sqrtx-3)^3 # using the chain rule? How do you find the derivative of #x*sqrt(x+1)#? #f(x) = 3(x+4)^5#-- the last thing we do before multiplying by the constant #3# is "raise to the #5th# power" -- use the chain rule. What is the derivative of #f(x) = sin (cos (tanx) )#? How do you find the derivative of #q(x) = (8x) ^(2/3)# using the chain rule? How do you differentiate #p = 2log_3(5^s) - log_3(4^s)#? If # A = 9/16(4r-sin(4r)) # and #(dr)/dt=0.7# when #r=pi/4# then evaluate # (dA)/dt # when #r=pi/4#? Are you sure you want to remove #bookConfirmation# How do you differentiate #f(x)=1/(x^sqrt(x-3))# using the chain rule? How do you find #f^37x# given #f(x)=cos3x#? The chain rule can be thought of as taking the derivative of the outer function (applied to the inner function) and multiplying it times the derivative of the inner function. What is the derivative of #ln(x^2+1)^(1/2)#? What is the derivative of #(4x)^3 * (2x)^6#? Converting customary units worksheet. How do you use the chain rule to differentiate #f(x)=(3x-9)^2(4x^3+2x^-9)^-9#? Use the Chain Rule to find the derivatives of the following functions, as given in Example 59. How do you differentiate #tan(cos^3(x))#? How do you differentiate #f(x)=ln(sine^(x^2))# using the chain rule? How do you find the derivative of #x(sqrt(2x-3))#? How do you differentiate #f(x) = ln(sqrt(arcsin(e^(2-x)) ) # using the chain rule? y = f(u) and u = g(x) and both dy/du and du/dx exists, then the derivative of the function . How do you use the chain rule to differentiate #y=5/(2x^3+3x)#? How do you find the derivative of #x^lnx#? If #f(x) =xe^x# and #g(x) = sin3x #, what is #f'(g(x)) #? How do you differentiate #e^((x^2-x)^2) # using the chain rule? How do you find the derivative of #sqrt(x^2-1)#? How do you use the chain rule to differentiate #y=((5x^5-3)/(-3x^3+1))^3#? What is the derivative of #f(x) = 8 π 9 #? SOLUTION 19 : Assume that h(x) = f( g(x) ) , where both f and g are differentiable functions. If #f(x) =cos3x # and #g(x) = (2x-1)^2 #, what is #f'(g(x)) #? How do you find the derivative of #y= 12((x^2-7)^(1/3))#? What is the first differential of #y= e^sinsqrtx# ? How do you find the derivative of a natural log exponential function #y = (ln(x^2))^(2x+3)#? The chain rule is often one of the hardest concepts for calculus students to understand. How do you find the derivative of #f(x) = tan^2(x)#? If #f(x)= cos(-2 x -1) # and #g(x) = 3x^2 -5 #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #y=[x(x+sin^2x)^3]^4#? Given #y=(sin(x))^(logx)# calculate #dy/dx# ? How do you differentiate # f(t)=sin^2(e^(sin^2t)# using the chain rule.? How do you differentiate #e^(2x^2-4x) # using the chain rule? How do you find the derivative of # (3+sin(x))/(3x+cos(x))#? We can … In these two problems posted by Beth, we need to apply not only the chain rule, but also the product rule. How do you find the derivative of #sqrt(5-3x)#? How do you use the chain rule to differentiate #root11(lnx)#? How do you use the chain rule to differentiate #sqrt(4x+9)#? If #f(x)= sqrt(x^2-1 # and #g(x) = 1/x #, what is #f'(g(x)) #? WHEN TO USE CHAIN RULE. How do you find #(d^2y)/(dx^2)# given #y+siny=x#? How do you differentiate #f(t)=sin^2(e^(sin^2t))# using the chain rule? How do you calculate the derivative of the function #f(x)=cos(x^3+x^2+1)#? How do you use the chain rule to differentiate #f(x) = cos(lnx)#? How do you differentiate #f(x)=(x^4 - 2x^2)^6# using the chain rule? What is the derivative of #y = 10^(1-x^2)#? The chain rule can be thought of as taking the derivative of the outer function (applied to the inner function) and multiplying it times the derivative of the inner function. What is the derivative of #T(w)=cot^3(3w+1)#? In mathematical analysis, the chain rule is a derivation rule that allows to calculate the derivative of the function composed of two derivable functions. How do you differentiate #f(x)=sqrtcos(1/(2x)^3)# using the chain rule? What is the derivative of #sqrt(4x² + 1)#? How do you find the derivative of #y= e^(2+x^3)# ? How do you use the chain rule to differentiate #1/-(4x)#? How do you find the derivative of #sqrt(1-x^2)#? How do you differentiate # y =-(e^(x-sin^2x)# using the chain rule? If. How do you differentiate #f(x)=((1/x)^2-x)# using the chain rule? If #f(x)= x^2-x # and #g(x) = 3x^( 2/3 ) #, what is #f'(g(x)) #? How do you differentiate #f(x)=csc(1/x^2-x) # using the chain rule? How do you differentiate #f(x)=sin(e^(x^2-2))# using the chain rule? Click HERE to return to the list of problems. How do you differentiate #f(x)=sec(3x^3-x^2 ) # using the chain rule? Then Instead of taking the derivative of #ln((a-x)/(a+x))# by the chain rule and quotient rule, can we use the laws of logarithms and take the derivative of #ln(a-x)-ln(a+x)#? How do you differentiate #f(x)=1-(3x-3)^2# using the chain rule.? What is the derivative of #(sqrt 6)/x^5# using the Power Rule? How do you differentiate # y= sin2x-cos2x# using the chain rule? This is for both equations. How do you differentiate #f(x)=sqrt(3+x^2) # using the chain rule? But I don't think that teaching that we need certain tools is helpful. How do you find the derivative of #y=(x^2+5)^2#? How do you use the chain rule to differentiate #y=sin(cosx)#? What is the derivative of #sin(3 - (pi)x)#? Let r(x)=f(g(h(x))), where h(1)=2, g(2)=3, h'(1)=4, g'(2)=5, and f'(3)=6, how do you find r'(1)? How do you find the 50th derivative of #y=cos2x#? 4 • (x 3 +5) 2 = 4x 6 + 40 x 3 + 100 derivative = 24x 5 + 120 x 2. How do you find the derivative of #(sin x)^(e^x)#? How do you differentiate #f(x)=e^cos(-2lnx)# using the chain rule? How do you use the chain rule to differentiate #y=tan(-2x)#? How do you differentiate #f(x)=(2x^5+3)cos(x^2)#? How do you find the derivative of #f(x)= cos (sin (4x))#? Is there an inverse chain rule for integration? If #f(x) =-sqrt(2x-1) # and #g(x) = 3/x^3 #, what is #f'(g(x)) #? How do you find the derivative of # f (x) = ln(1 - sin x)#? How do you use the chain rule to differentiate #y=(3x-1)(-3x^2-4)^-3#? If #f(x)= sec 9x # and #g(x) = sqrt(2x-3 #, how do you differentiate #f(g(x)) # using the chain rule? Decimal representation worksheets. How do you differentiate #f(x)=sin(6x+5x^2+1)# using the chain rule? How do you use the chain rule to differentiate #y=7/(2x+7)^2#? What is the derivative of # x * ((4-x^2)^(1/2))#? How do you find the derivative of # lnx / x#? What is the derivative of #(sqrt(x+13)) / (x-4)(root3(2x+1))#? If #F(x)=f(xf(xf(x)))# where f(1)=2, f(2)=3, f'(1)=4, f'(2)=5, and f'(3)=6, how do you find F'(1)? How do you use the chain rule to differentiate #(ln4x)^100#? How do you differentiate # f(x)=sqrt(ln(x^2+3)# using the chain rule.? How do you differentiate #f(x)=sin(1/(3x-1))# using the chain rule? How do you differentiate # f(x)=e^sqrt(ln(1/sqrtx)# using the chain rule.? How do you differentiate #f(x)=csc(ln(1/x)) # using the chain rule? Chain rule is also often used with quotient rule. How do you find the derivative of #y = [e^(-1) + e^(t)]^3#? How do you differentiate #f(x)=tan(5x^3)#? How do you find the derivative of #f(x)= (x+sinx)/(cosx) #? If #f(x) =tan^2x # and #g(x) = sqrt(5x-1 #, what is #f'(g(x)) #? How do you find the derivative of #g(x)=(2x^2+x+1)^-3#? How do you find the derivative of #(cos x)^2 - cos x#? How do you differentiate #f(x)=sin(cos(tanx))# using the chain rule? How do you differentiate #cossqrtxsqrt(cosx)#? How do you find the derivative of #y=(3x^5 - 4x^3 + 2)^23# using the chain rule? If g is twice differentiable function and #f(x)=xg(x^2)#, how do you find f'' in terms of g, g', and g''? What is the derivative of #(cos x)^(sin x)#? How do you differentiate # y= 3y^4-4u+5 ;u=x^3-2x-5 # using the chain rule? If #f(x)= cos(-2 x -1) # and #g(x) = 4x^2 -5 #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the derivative of #g(t) = 1/t^(1/2)#? How do you differentiate #y = cos(cos(cos(x)))#? If #f(x)= sec2 x # and #g(x) = -x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? A few are somewhat challenging. How do you differentiate #f(x)=x-sqrt(2^x-x^2)# using the chain rule? How do you differentiate # y =1/sqrtln(x^2-3x)# using the chain rule? How do you differentiate #f(x)=sqrttan(2-x^3) # using the chain rule? How do you differentiate #f(x)=sin(e^(3-x)) # using the chain rule? How do you find the derivative of #y = 9tan^-1(x − (sqrt (1 + x^2))#? What is the second derivative of #f(cosx)# when #x=pi/2# where #f(x)=sinx#? How do you differentiate # y =x /sec ^2x^3# using the chain rule? Converting customary units worksheet. How do you differentiate #f(x)=sin^2(lnx)xcos^2(x^2)# using the chain rule? What is the derivative of #sqrt(x^2+2x-1)#? How do you differentiate #f(x)=1/(ln(1-(e^(-cos(x^2)))))^(3/2)# using the chain rule? How do you differentiate #f(x)= ln(2x+1)^(-1/2) #? How do you use the chain rule to differentiate #ln(tanx)#? How do you differentiate #f(x)=cos(e^(x) ) # using the chain rule? In calculus, the chain rule is a formula to compute the derivative of a composite function. How do you differentiate #f(x) = ln(1/sqrt(arcsin(e^(x)) ) ) # using the chain rule? How do you find the derivative of #g(x)=3(2-5x)^6#? Caculus question on finding deriavatives? How do you differentiate #f(x)=sqrt(ln2x)# using the chain rule? How do you find the derivative of #f(x)=(x^5+6x^2-1)(1-3x)^2#? Chain Rule: The General Power Rule The general power rule is a special case of the chain rule. How do you differentiate #f(x)=sec(-e^(sqrtx) ) # using the chain rule? How do you use the chain rule to differentiate #(sqrtx)^10#? How do you find the derivative of #f(x)=ax^2+bx+c#? How do you differentiate # f(x)=(7-8x^3)^2# using the chain rule.? If #f(x) =-e^(-3x-7) # and #g(x) = lnx^2 #, what is #f'(g(x)) #? If #f(x) =-e^(x) # and #g(x) = tan^2x^2 #, what is #f'(g(x)) #? How do you differentiate #f(x)=sqrt(sin^2x^2 - cos^3x)# using the chain rule? The chain rule is by far the trickiest derivative rule, but it’s not really that bad if you carefully focus on a few important points. If #f(x)= 1/x # and #g(x) = 1/x #, what is #f'(g(x)) #? The chain rule lets us "zoom into" a function and see how an initial change (x) can effect the final result down the line (g). How do you differentiate # y =cos^3(5x^2-2)# using the chain rule? How do you differentiate #f(x)=(3x-cos^3x)^2/4# using the chain rule? How do you differentiate # y=cos^-1(1-2x^2)#? What is the derivative of #f(x)=ln (x^2+2)#? How do you find the derivative of #f(x) = (x^2+1)^3#? How do you use the chain rule to differentiate #y=(7-x)^4#? How do you use the chain rule to differentiate #y=(2x-7)^3#? How do you find the derivative of #y= root3(e^x+1)# ? If #f(x)= sin3x # and #g(x) = 2x^2 -3x #, how do you differentiate #f(g(x)) # using the chain rule?