How do you differentiate # y =sin(ln(cos x)) # using the chain rule? How do you use the chain rule to differentiate #y=-5/(3x^2-4)^6#? In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x) . How do you find the derivative of #y= e^sqrt(x)# ? How do you differentiate #f(x)=sec^2(e^(x^4) ) # using the chain rule? How do you find the derivative of #f(x) = x + sqrt(x)#? How do you differentiate # f(x) = (x - 1)^4 /(x^2+2x)^5# using the chain rule? How do you differentiate #e^((x^2-x)^2) # using the chain rule? How do you differentiate #f(x) = 1/sqrt(sin^2(2-x^2) # using the chain rule? How do you find the derivative of #F(x) = sqrt( (x-8)/(x^2-2) )#? What is the derivative of #y = a^9 + (cos(x))^9#? Are you sure you want to remove #bookConfirmation# How do you differentiate #f(x)=sin(x^3)#? Is there an inverse chain rule for integration? How do you use the chain rule to differentiate #sin(e^(6x))#? How do you use the chain rule to differentiate #y=(x+1)^6/(3x-2)^5#? How do you differentiate #f(x)=1/e^sqrt(1-(3x+5)^2)# using the chain rule.? How do you differentiate #f(x)=sec^4(e^(x^3) ) # using the chain rule? How do you use the chain rule to differentiate #y=(x^2+4)^-1#? Example. How do you differentiate # y = 4(x-(3-5x)^4)^2# using the chain rule? How do you differentiate #f(x)=cos(tanx)# using the chain rule? How do you find the derivative of #f(x) = sin^2 x#? How do you differentiate #f(x)=sqrt(cos^3(3x-2))# using the chain rule? How do you find the derivative of #f(x) = x + x^(1/2)#? © 2020 Houghton Mifflin Harcourt. How do you differentiate #f(x)=x(3x-9)^3# using the chain rule? How do you differentiate #r/(r^2 + 1)^(1/2)#? How do you find the derivative of #(1-y^2)^(1/2)#? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #g(t)=1+2cos(((2pi)/5)(t-3))# using the chain rule? How do you differentiate #f(x)=sqrt(ln2x)# using the chain rule? How do you differentiate #sin((2sqrtx+1)/(x+1))#? How do you find the derivative of #f(x) = 4e^(3x+2)#? How do you differentiate #f(x)=-5 xe^(x/cos x)# using the chain rule? How do you use the chain rule to differentiate #y=4/(sqrt(x-5)#? How do you differentiate #f(x) = (x^3+cos3x)^(1/2)?# using the chain rule? How do you differentiate #arc cot(-4sec(1/(3x^2)) )# using the chain rule? How do you differentiate #f(x)=e^(csc(2/x)# using the chain rule.? What is the derivative of this function #sin(x+1)#? How do you differentiate #f(x)=sqrt(((3x^2-x^3)/(x-3x^2))# using the chain rule? How do you find the derivative of #f(x) = (ln x)^2#? How do you differentiate #f(t)=root3(1+tant)#? Are they simply different forms of each other? How do you find the derivative of #v=4(2x^2-x+3)^-2#? How do you find the derivative of #f(x)= 1/(9x+6)^2#? How do you use the chain rule to differentiate #y=((x+1)/(x-2))^5#? How do you use the chain rule to differentiate #y=((x^5+4)/(x^2-5))^(1/5)#? How do you differentiate #(5-x^-1)^(1/3)#? How do you differentiate # y =- ln( x^2 - x +4) # using the chain rule? If #f(x)= - e^(5x # and #g(x) = 3 x #, how do you differentiate #f(g(x)) # using the chain rule? y = tan^4(3x)#? What is the derivative of #ln((x^2-4)/(2x+5))#? How do you find the derivative of #w=(1+4x^3)^-2#? How do you determine #(dy)/(dx)# given #f(x)=(3x^4-7)^10#? If #f(x) =sin(-x/4) # and #g(x) = sqrt(x^3+3 #, what is #f'(g(x)) #? This rule allows us to differentiate a vast range of functions. If #f(x) =cos3x # and #g(x) = (x+3)^2 #, what is #f'(g(x)) #? Eg: (26x^2 - 4x +6) ^4 * Product rule is used when there are TWO FUNCTIONS . How do you find the derivative of #sqrt(1/x^3)#? How do you differentiate #arcsin(csc(4x)) )# using the chain rule? If #f(x) =-e^(x) # and #g(x) = 3csc^2x^2 #, what is #f'(g(x)) #? Solution for dw Use chain rule to find dt if w = xez, x = t², y = 1- t, z = 1+ 2t. How do you differentiate # f(x)=e^sqrt(1/x)# using the chain rule.? How do you find the derivative of #sqrt(7x)#? Step 1 Differentiate the outer function. How do you differentiate #f(x)=cot(e^(1/x)) # using the chain rule? How do you differentiate #f(x)=1/sqrtsec(e^(x) ) # using the chain rule? How do you differentiate #f(x)=sqrt(cose^(4x)# using the chain rule.? If #f(x)= x^2-x # and #g(x) = x^( 1/3 ) #, what is #f'(g(x)) #? If #f(x)= sin6 x # and #g(x) = e^(3+2x ) #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=cos(7-4x) # using the chain rule? How do you find the derivative of #y= e^(2+x^3)# ? How do you differentiate #f(x)=cot(sqrt(x-3)) # using the chain rule? How do you differentiate #f(x) = 4/(x+1)^2# using the chain rule? How do you differentiate #f(x)=(2x-cos^3x)^2-(lnx)^2# using the chain rule? How do you differentiate #f(x)=sin(4-x^2) # using the chain rule? How do you use the chain rule to differentiate #y=(x+2)^4#? How do you differentiate #f(x)=ln(x^2)# using the chain rule? How do you differentiate # f(x)=e^sqrt(3x+x^2)# using the chain rule.? {\displaystyle '=\cdot g'.} How do you use the chain rule to differentiate #y=cos(sqrt(8t+11))#? How do you use the chain rule to differentiate #y=(x-1/x)^(3/2)#? 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)=sin^2(sqrt(3x/(x-1)^2))*cos2x # using the chain rule? How do you differentiate #f(x)=sec(e^(sqrtx-4) ) # using the chain rule? How do you differentiate #(e^ (2x) - e^(-2x) ) ^ 2#? How do you find the derivative of #sqrt(4+x^2)#? How do you find the derivative of #(arctan x)^3#? How do you differentiate given # 12(sin5x)^3#? How do you find the derivative of the function #f(x)=sqrt(1+2x)#? How do you differentiate # y =sqrt( x + sqrtx )# using the chain rule? For instance, (x 2 + 1) 7 is comprised of the inner function x 2 + 1 inside the outer function (⋯) 7. How do you differentiate #f(x)=sqrt(tane^(4x)# using the chain rule.? How do you differentiate #f(x)=ln(3(e^(sin^2x))^4)# using the chain rule? Example 5: Find the slope of the tangent line to a curve y = ( x 2 − 3) 5 at the point (−1, −32). How do you find the derivative of # y = sin(x cos x)# using the chain rule? Thus, the slope of the line tangent to the graph of h at x=0 is . #y=((1+x)/(1-x))^3=((1+x)(1-x)^-1)^3=(1+x)^3(1-x)^-3#. How do you find the derivative of #y=(4x+3)^-1+(x-4)^-2#? How do you differentiate # f(x)=ln(1/sqrt(xe^x-x))# using the chain rule.? How do you differentiate # f(t)=-e^(sin(pi/x))sinpix # using the chain rule.? How do you use the chain rule to differentiate #r=sec2thetatan2theta#? How do you find the derivative of #cos(1-2x)^2#? Click HERE to return to the list of problems. Then when the value of g changes by an amount Δg, the value of f will change by an amount Δf. How do you find the derivative of #y = cos^3(3x+1)#? How do you differentiate #f(x)=csce^(4x)# using the chain rule.? How do you differentiate #f(x)=ln((x-1)/(x^2+1))#? How do you find #(dy)/(dx)# given #x^3+y^3=3xy^2#? How do you differentiate #f(x)=sin((x/(x^2-1))^(3/2))# using the chain rule? How do you differentiate #y= -cos^-1 (1/x^5)#? How do you use the chain rule to differentiate #ln(tanx)#? How do you differentiate #y = ln [x^4 sin^2 (x)]#? Step 3 (Optional) Factor the derivative. How do you use the chain rule to differentiate #y=(5x^3-3)^5root4(-4x^5-3)#? How do you differentiate #f(x)=sqrt((1-4x)^3# using the chain rule.? How do you differentiate # y =cos^3(5x^2-2)# using the chain rule? What is the derivative for #f(x)=sqrt(x^2-1)#? Since the functions were linear, this example was trivial. How do you differentiate #f(x)=csc(2x -4) # using the chain rule? How do you differentiate #f(x)=(x^2+4x+6)^5#? What is the derivative of #ln(sqrt(sin(2x)))#? How do you find the derivative of #y=arcsin(5x+5)#? How do you find f' if #f(x)=cos^2(3sqrt x )#? What is the derivative of #ln ((x^2 +1) /(2x))#? How do you differentiate # y= sqrt((3x)/(2x-3))# using the chain rule? How do you differentiate #sin(x^2)(cos(x^2))#? What is the derivative of #sin(3 - (pi)x)#? How do you differentiate # y =sqrt((3x-9)^3 # using the chain rule? What is the derivative of #3*sqrtx - sqrt(x^3)#? How do you find the derivative of #(t^3+1)^100# using the chain rule? If #f(x) =csc^3(x/2) # and #g(x) = sqrt(2x+3 #, what is #f'(g(x)) #? How do you use the chain rule to differentiate #y=sqrt(3x^2+4x)#? How do you find the derivative of #e^ [2 tan(sqrt x)]#? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of # [((3x-1)^4)((2x+1)^-3)]# using the chain rule? How do you differentiate #sqrt((x+1)/(2x-1))#? How do you differentiate #f(x)=tan(1-3x^2) # using the chain rule? How do you differentiate #f(x)=e^tan(1-x^2) # using the chain rule? How do you differentiate # f(x)= [(2x-5)^5]/[(x^2 +2)^2] # using the chain rule.? If #f(x)= cot2 x # and #g(x) = e^(-3x ) #, how do you differentiate #f(g(x)) # using the chain rule? The chain rule is often one of the hardest concepts for calculus students to understand. How do you use the chain rule to differentiate #y=(x+1)^(-1/2)#? How do you use the chain rule to differentiate #y=3xsin(6x)#? How do you find the derivative of #f(x) = tan(sinx)#? How do you differentiate #f(x) = 1/sqrt(arctan(e^x-1) # using the chain rule? How do you find the derivative of #y=tanh(6+e^(6x))#? We will have the ratio How do you differentiate #f(x)=tan(5x^3)#? #f'(x)=?# How do you use the chain rule to differentiate #y=((x+5)^5-1)^4#? 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. How do you find the derivative of #f(x)= (x+sinx)/(cosx) #? How do you differentiate # f(x)=e^sqrt(ln(1/sqrtx)# using the chain rule.? How can I simplify this expression ? How do you differentiate #f(x)=e^(csc2x)# using the chain rule.? How do you differentiate #f(x)=sece^(4x)# using the chain rule.? How do you differentiate # y =1/sqrtln(x^2-3x)# using the chain rule? Using the point-slope form of a line, an equation of this tangent line is or . Most of the examples in this section won’t involve the product or quotient rule to make the problems a little shorter. How do you find the derivative of #y= sqrt((x-1)/(x+1))# ? How do you differentiate #3sin^2(3x) # using the chain rule? How do you differentiate #f(x)=ln(1/sin(3x))# using the chain rule? Here z is the function of y, z = f(y) and y is a function of x, y= g(x) Using the previous formula, we can rewrite the differential equation as follows: Let us understand this better with the help of an example. How do you differentiate # arctan(x^2+1)#? How do you differentiate #f(x)=(x/sin(7x))^2# using the chain rule? What is the derivative of #cos[sin^-1 (2w)]#? How do you find the derivative of #(sin x)^(e^x)#? Now, let's differentiate the same equation using the chain rule which states that the derivative of a composite function equals: (derivative of outside) • (inside) • (derivative of inside). How do you find the derivative of #f(x)=(8x^2-6)^-1#? How do you use the chain rule to differentiate #y=root3(-2x^4+5)#? How do you differentiate # f(x)=e^sqrt(lnsqrtx)# using the chain rule.? How do you differentiate #e^((2-sqrtx)^2) # using the chain rule? How do you find the first derivative of #e^(x^2)#? Most problems are average. How do you find the primitive function of #f(x)=1/sqrt(3-x)# and #f(x)=(4-2x)^-2# ? How do you use the chain rule to differentiate #y=(2x-1)^4/(x+1)^2#? How do you use the chain Rule to find the derivative of #sqrt(2x^3 - 3x- 4)#? How do you differentiate #sqrt(cos(x^2+2))+sqrt(cos^2x+2)#? How do you differentiate #f(x)= (4x^5+5)^(1/2)# using the chain rule? How do you differentiate # y=sec (3 - 8x)# using the chain rule? ... BODMAS Rule. What is the derivative of #f(x)=(4/3)pi^3#? How do you find the derivative of #sqrt(e^(2x) +e^(-2x))#? How do I find the derivative of #y=ln(secx + tanx)#? How do you use the chain rule to differentiate #(e^(6x))^10#? How do you use the chain rule to differentiate #y=(x+1)^(1/2)#? How do you differentiate #f(x) = sqrt[ (3 x + 1) / (5 x^2 + 1)# using the chain rule? What is the derivative of #ln(1+(1/x))#? How do you use the chain rule to differentiate #y=(-5x^3-3)^3#? How do you differentiate #y=sqrt(x-1)+sqrt(x+1)#? However, we rarely use this formal approach when applying the chain rule to … What is the derivative of #(sqrt(x+13)) / (x-4)(root3(2x+1))#? If #f(x) =tan^24x # and #g(x) = sqrt(5x-1 #, what is #f'(g(x)) #? How do you differentiate #y=sqrt(4x +3)#? How do you differentiate #f(x)=(3x-cos^3x)^2/4# using the chain rule? How do you determine #(dy)/(dx)# given #y=sec(sqrt(x^3+x))#? How do you use the chain rule to differentiate #tan(ln(4x))#? How do you differentiate #f(x)=sqrtcos(1/(2x)^3)# using the chain rule? How do you find the derivative for #y=(x+1/x-1)^2#? What is the derivative of #sqrt(x^2-2x+1)#? How do you differentiate #f(x)=sqrt(e^(cot(1/x)# using the chain rule.? How do you differentiate #y=sqrt(2-e^x)#? How do you find the derivatives of the function #f(x) = sin(x^2)#? How do you differentiate #f(x)=e^(cscsqrtx)# using the chain rule.? How do you differentiate #f(x)=e^(cossqrtx)# using the chain rule.? How do you find the derivative of #y= x*sin(1/x)# ? How do you find the derivative of #f(x)=(5x^6sqrt x) + (3/(x^3 sqrt x))#? How do you find the derivative of #y=2(5x+3)^7-1# using the chain rule? What is the derivative of #f(x) = sec(5x)#? How do you find the derivative of #sin(x cos x)#? How do you differentiate # y =sqrt(sec ^2x^3# using the chain rule? How do you differentiate #f(x)=(2x^5+3)cos(x^2)#? How do you differentiate #y=(x^2+1)root3(x^2+2)#? How do you differentiate #f(x)=sec(1/sqrtx ) # using the chain rule? How do you differentiate # y=1/ln(x^3-x^2)-ln(1/(x^3-x^2))# using the chain rule? What is the derivative of #f(x) = 8 π 9 #? How do you differentiate #ln(x^2+1)^(1/2)#? How do you differentiate #f(x) = 4/sqrt(tan^2(1-x) # using the chain rule? If you're seeing this message, it means we're having trouble loading external resources on our website. Let us find the derivative of . How do you use the chain rule to differentiate #(-cosx)^2008#? How is the chain rule different from the product rule? How do you find the derivative of #sqrt(e^x)#? What is the derivative of #f(x)= ln (2x^3 +1)#? How do you differentiate #y = (sec x) (tan x)#? What is the derivative of # ( cos (pi*x) +1 ) / x#? How do you find the derivative of #3(x^2-2)^4#? How do you find the derivative of #3*(sqrtx) - (sqrtx^3)#? Example 59 ended with the recognition that each of the given functions was actually a composition of functions. How do you differentiate #f(x)=cos(-3x^2+2)^2#? How do you use the chain rule to differentiate #y=(x^2+4x)^(1/2)#? Differentiate with respect to x #e^tanx/x^(1/2)# ? How do you differentiate #f(x)=e^cos(-2lnx)# using the chain rule? For instance, if you had sin(x^2 + 3) instead of sin(x), that would require the chain rule. How do you differentiate #f(x)=ln((x^3-x ^2 -3x + 1) ^(2/5))# using the chain rule? How do you use the chain rule to differentiate #y=(x^2+1)^(1/2)#? How do you find the derivative of #f(x)=7^(2x)#? How do you differentiate #f(x)=csc(sqrt(x^2-5x)) # using the chain rule? How do you find the derivative of #root4(lnx)#? The chain rule applies whenever you have a function of a function or expression. What is the derivative of #f(x)=e^(2x) ln(x+2)#? If #f(x)= tan8 x # and #g(x) = e^(-3x ) #, how do you differentiate #f(g(x)) # using the chain rule? Step 1. How do you differentiate # y = 2/[(e^(x) + e^(-x)]#? How do you find the derivative of #q(x) = (8x) ^(2/3)# using the chain rule? How do you differentiate #y = (sin(3x) + cot(x^3))^8#? How do you differentiate #e^((2-x)^2) # using the chain rule? Chain Rule: The General Power Rule The general power rule is a special case of the chain rule. How do you differentiate # y = (6e^(-7x)+2x)^2# using the chain rule? How do you differentiate # y =4x ln(3x + 2)# using the chain rule? How do you differentiate # f(x)=1/sqrt(ln(xe^x))# using the chain rule.? How do you find the derivative of #y=6sin(2t) + cos(4t)#? How do you use the chain rule to differentiate #sqrt(-cosx)#? What is the derivative of #w =sqrt(x^2+y^2+z^2)#? What is the derivative of #ln[(x(x^2+1)^2)/(2x^3-1)^(1/2)] #? If #f(x) =-e^(-3x-7) # and #g(x) = -2sec^2x #, what is #f'(g(x)) #? How do you differentiate #y=(e^(2x)+1)^3#? How do you find the derivative of #x^(3/x)#? How do you differentiate #sqrt(sin^3(2x^2) # using the chain rule? If f(x) and g(x) are functions such that #f(3)=2, f'(3)=1,g(3)=0,# and #g'(3)=4#. Can you explain how the chain rule work in real life? How do you use the chain rule to find the derivative of log x? How do you differentiate #f(x)=xsin(1/x)#? What is the derivative of #(xe^-x)/(x^3+x)#? How do you find the derivative of #y=ln(e^x+3)# ? How do you differentiate #f(x)=csc(1/(5x^2-1))# using the chain rule? How do you differentiate #f(x)=1/(ln(1-(e^(-cos(x^2)))))^(3/2)# using the chain rule? How do you find the derivative of #sqrt (x^2 +1)#? Indeed, we have So we will use the product formula to get 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 #g(x)=(1+4x)^5(3+x-x^2)^8#? How do you calculate the derivative for #y = 3(5 - x^2)^5#? Here, three functions— m, n, and p—make up the composition function r; hence, you have to consider the derivatives m′, n′, and p′ in differentiating r( x). How do you differentiate #f(x)=csc(5x) # using the chain rule? How do you differentiate #f(x)=x * (4-x^2)^(1/2)# using the chain rule? How do you differentiate # y =(3x-2)^10 # using the chain rule? How do you use the chain rule to differentiate #y=4(x^2+1)^2#? How do you differentiate #f(x)=sec^2x-tan^2x#? • Solution 2. How do you differentiate #f(x)=(2x-3)^3# using the chain rule? All rights reserved. How do you differentiate #f(x)=sqrt(xsin(ln(x)^3)# using the chain rule? How do you differentiate #f(x)=e^(-x^2-2x+1) # using the chain rule? How do you use the chain rule to differentiate #y=(x^4+3x)^-2#? SOLUTION 19 : Assume that h(x) = f( g(x) ) , where both f and g are differentiable functions. What is the derivative of #sin(x(pi/8))#? How do you differentiate # (e^(2x) + 2x) ^0.5#? Confirm that U (ξ, η) =-1 4 η-1 24 η 2 + 1 4 ξ + 3 8 ξ 2 is a solution of this canonical PDE and that it satisfies the required prescribed data. How do you differentiate #y=cot^2(sintheta)#? How do i find the first and second derivative of this problem #f(x)=(2x^2+2)^7/2#? If #f(x) =-e^(x) # and #g(x) = tan^2x^2 #, what is #f'(g(x)) #? How do you find the derivative of #(cos^2(t) + 1)/(cos^2(t))#? How do you find the derivative of #(cosx)(sinx)#? PEMDAS 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 find the derivative of #sqrt(9-x)#? The key is to look for an inner function and an outer function. How do you differentiate #f(x)=cos(x^3)#? How do you determine #(dy)/(dx)# given #y=cos(1-x)#? What is the derivative of #(sqrt 6)/x^5# using the Power Rule? How do you use the chain rule to differentiate #y=cos^7(pit-16)#? How do you differentiate # y =-2e^(xcosx)# 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? What is the derivative of #y=ln(x^4sin^2x)#? And, sure enough, the hard thing can be to choose the right tool. How do you differentiate #f(x) = sqrt(sin(4x) # using the chain rule? The composition of two functions [math]f[/math] with [math]g[/math] is denoted [math]f\circ g[/math] and it's defined by [math](f\circ g)(x)=f(g(x)). How do you differentiate #h(x) = (6x-x^3)^2#? How do you differentiate # f(x)=e^((6x-2)^2 # using the chain rule.? How do you differentiate #f(x)=sqrt(1/x^2)# using the chain rule? What is the derivative of #sin^2 x + cos^2 x#? 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. How do you differentiate #f(x)=ln(x^2-sqrt(2x+8)))# using the chain rule? How do you find the derivative of #cos^2(x^3)#? If #f(x) =-sqrt(3x-1) # and #g(x) = (2-1/x)^2 #, what is #f'(g(x)) #? If #f(x) =-e^(-3x-7) # and #g(x) = lnx^2 #, what is #f'(g(x)) #? Example 2: Find f′( x) if f( x) = tan (sec x). How do you find the derivative of #r= 2theta sqrt(sec theta)# using the chain rule? If #f(x) = -x^2 -2x# and #g(x) = e^(x)#, what is #f'(g(x)) #? How do you differentiate # f(x)=(1-e^x)^2# using the chain rule.? The chain rule is a method for finding the derivative of composite functions, or functions that are made by combining one or more functions.An example of one of these types of functions is \(f(x) = (1 + x)^2\) which is formed by taking the function … WORKSHEETS. How do you find the derivative of the function #y = sin(tan(5x))#? How do you differentiate #y=sqrtx+1+1/sqrtx#? How do you differentiate #f(x)=sqrtsin(2-4x) # using the chain rule? How do you differentiate # 3/4 * (2x^3 + 3x)^(-1/4)#? Use the chain rule to calculate h′(x), where h(x)=f(g(x)). How do you find the derivative of # pi^(x+2)# using the chain rule? How do you differentiate #f(x)=cos3x^(1/3)# using the chain rule? Using the chain rule to relate inverse function's derivative to function's derivatives. How do you differentiate #f(x)=tane^(4x)# using the chain rule.? How do you differentiate #y = 2^xlog_2(x^4)#? How do you find the derivative of #ln(sqrt(sin(2x)))#? Basic examples that show how to use the chain rule to calculate the derivative of the composition of functions. The chain rule can be tricky to apply correctly, especially since, with a complicated expression, one might need to use the chain rule multiple times. How do you use the chain rule to differentiate #y=(x^2+3)^4#? How do you differentiate #f(x)=e^tan(x) # using the chain rule? What is the derivative of #T(w)=cot^3(3w+1)#? What is the derivative of #y = cos(cos(cos(x)))#? How do you differentiate #f(x)=cot(3x) # using the chain rule? The chain rule is one of the toughest topics in Calculus and so don't feel bad if you're having trouble with it. How do you differentiate #f(x)=1/sin(sqrt(1/x))# using the chain rule? How do you differentiate # f(x)=e^(x-(x-2)^2 # using the chain rule.? How do you differentiate #f(x)=e^(5x^2+7x-13)#? One way to do that is through some trigonometric identities. We’ve been using the standard chain rule for functions of one variable throughout the last couple of sections. How do you differentiate #f(x)=sqrt(e^cot(x)) # using the chain rule? If #f(x)= cos 4 x # and #g(x) = -3x #, how do you differentiate #f(g(x)) # using the chain rule? Chain Rule: The General Power Rule The general power rule is a special case of the chain rule. How do you find the derivative of #ln(x^2+1)#? Before stating the result rigorously, consider a simple case using indefinite integrals. Take an example, f (x) = sin (3x). How do you differentiate #tan(cos^3(x))#? How do you differentiate #f(x)=sec(4x^5)#? What is the first differential of #y = t^(3/2)(16-sqrtt)#? How do you differentiate #y = 6 cos(x^3 + 3)#? What is Derivative Using Chain Rule.
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