How do you use the chain rule to differentiate #y=sqrt(3x^2+4x)#? How do you find the derivative of #f(x)=2/(6x+5x+1)^2#? WHEN TO USE CHAIN RULE. How do you differentiate #f(x)=ln(sine^(x^2))# using the chain rule? How do you find the derivative of #2sec((3x+1)^(1/2))#? How do you differentiate #f(x)=sin(1/sqrt(3x^2-4) ) # using the chain rule? Is there more than one way to differentiate #(2x+1)^2/(2x+4)#? If #f(x)= tan8 x # and #g(x) = e^(5x ) #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=sece^(4x)# using the chain rule.? How do you differentiate #ln (tan (x^2))#? Use the chain rule twice?? How do you differentiate #f(x)=(x^2+4x+6)^5#? How do you use the chain rule to differentiate #y=cos((4x)^3)#? How do you differentiate #f(x)=x/ln(sqrt(1/x))# using the chain rule? The chain rule is used when you want to differentiate a function to the power of a number. How do you differentiate #f(x) = 4/sqrt(tan^2(1-x) # using the chain rule? h(x) = g(x) / 1 + f(x), Differentiate the function? How do you differentiate #f(x)=sqrt((1-xe^(2x))^3# using the chain rule.? What is the derivative of #ln(x^2)+5^(2x)#? How do you differentiate #f(x)=sec(e^(sqrtx-4) ) # using the chain rule? How do you differentiate #f(x) = ln(sqrt(arcsin(e^(2-x^2)) ) # using the chain rule? How do you use the chain rule to differentiate #y=2(x^3-x)^-2#? How do you find the derivative of #ln(x^2+1)#? The chain rule states formally that . y = tan^4(3x)#? How do you differentiate # f(x)=1/(e^((lnx-2)^2 ))# using the chain rule.? If #f(x) =cos3x # and #g(x) = (x+3)^2 #, what is #f'(g(x)) #? How do you differentiate #f(x)=xsinsqrtx# using the chain rule? How do you differentiate #f(x)=e^(cscsqrtx)# using the chain rule.? How do you find the derivative of #x/ sqrt (x^2 +1)#? How do you differentiate #f(x)=sqrt(e^(cot(1/x)# using the chain rule.? if #v=1148sqrt(p)# where #p# is a function of #t# then find #(dv)/dt# when #p=44.0# and #dp/dt=0.307#? We will have the ratio How do you differentiate #y=(x^4+3x^2-2)^5#? If #f(x) =csc^3(x/2) # and #g(x) = sqrt(2x+3 #, what is #f'(g(x)) #? How do you differentiate #f(x)=csc(ln(1/x)) # using the chain rule? If #f(x) =xe^x# and #g(x) = sinx-x#, what is #f'(g(x)) #? How do you find the derivative of #f(x)= cos (sin (4x))#? Before we discuss the Chain Rule formula, let us give another example. How do you find the 50th derivative of #y=cos2x#? If #f(x)= csc7 x # and #g(x) = e^(1 +3x ) #, how do you differentiate #f(g(x)) # using the chain rule? y = (ln(1 + e^x))^5, Differentiate the function? What is the derivative of # (ln (x-4)) ^ 3#? 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 #(x^2 + 1/x)^5#? How do you find the derivative of # [((3x-1)^4)((2x+1)^-3)]# using the chain rule? What is the derivative of #sqrt(x - 1)/sqrtx#? What is the second derivative of #f(cosx)# when #x=pi/2# where #f(x)=sinx#? How do you differentiate # y =- ln( x^2 - x +4) # using the chain rule? How do you differentiate #f(x)=sec(1/(5x^2-1))# using the chain rule? How do you use the chain rule to differentiate #y=2(x^4+x)^-1#? How do you use the chain rule to differentiate #f(x)=(x^7-3x^2+15x^(-3/2))^6#? How do you differentiate #f(x)=cos3x^(1/3)# using the chain rule? How do you find the derivative of #f(x)=sin (1/x^2)# using the chain rule? How do you find the derivative of #y=tan(5x)# ? How do you differentiate #f(x) = 4/(x+1)^2# using the chain rule? How do you differentiate #arc cot(-4sec(1/(3x^2)) )# using the chain rule? What is the derivative of #z=sin^3(theta)#? What is the derivative of # (x^4+3x^2-2)^5#? Notice that this function will require both the product rule and the chain rule. How do you find the second derivative of #y=x^5#? How do you use the chain rule to differentiate #y=cos^6x#? How do you find the derivative of #h(x) = cos(4x^3)#? How do you find the derivative of #f(x)=1/(2x+5)^5#? $\begingroup$ @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 #s=[(t^2+1)^3+t]^-1#? How do you differentiate #f(x)=(1/(x-3)^2)^2# using the chain rule? How do you differentiate #y= ln e^(6x+1)#? This calculator … How do you use the chain rule to differentiate #f(x) = cos(lnx)#? 3) You could multiply out everything, which takes a bunch of time, and then just use the quotient rule. 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. Differentiate with respect to x #e^tanx/x^(1/2)# ? How do you use the chain rule to differentiate #y=sin^3(2x+1)#? How do you differentiate # f(x)=sqrt(ln(x^2+3)# using the chain rule.? which represents the slope of the tangent line at the point (−1,−32). How do you differentiate #f(x)=sqrt(cot(x)) # using the chain rule? The chain rule is a rule for differentiating compositions of functions. How do you differentiate #sin(x^2)(cos(x^2))#? How do you differentiate # y =cos^3(5x^2-2)# using the chain rule? If #f(x)= - x^2 + x # and #g(x) = sqrtx + x #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the derivative of #(ln tan(x))^2#? How do you differentiate #f(x)=(2x+3)^4 / x# using the chain rule? How do you find the derivative of #y=ln(sin2x)#? How do you differentiate #f(x) = (3x+7)^5?# using the chain rule? A few are somewhat challenging. WORKSHEETS. How do you find the derivative of #f(x)=(5x^6sqrt x) + (3/(x^3 sqrt x))#? How do you differentiate # y =sin(ln(cos x)) # using the chain rule? How do you differentiate # y =1/sqrtln(x^2-3x)# using the chain rule? How do you differentiate #y= 2 sin ^-1 (4x^4)#? What is the derivative of #sqrtthetasintheta#? How do you use the chain rule to differentiate #f(x)=sin(1/(x^2+1))#? How do you use the chain rule to differentiate #y=(cosx/(1+sinx))^5#? What is the derivative of #-(5-x^2)^(1/2) #? How do you use the chain rule to differentiate #y=(x^2+5x-2)^2#? How do you differentiate #f(t)=sin^2[e^(sin^2)t]#? What is the derivative of #y= (cos pi x)/(sin pi x + cos pi x)#? How do you differentiate #f(x)=e^tan(1-x^2) # using the chain rule? How do you find f ' if #f(x)=sin (1/x^2)#? (3 + +? If #f(x)= (5x -1)^3 # and #g(x) = 3x^( 2/3 ) #, what is #f'(g(x)) #? How do you differentiate #cossqrtxsqrt(cosx)#? How do you find the derivative of #e^(x-1)#? How do you differentiate #f(x) =xsec4x^3 # using the chain rule? How do you differentiate #f(x) = 1/sqrt(arctan(e^x-1) # 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 use the chain rule to differentiate #y=tan^4x#? How do you use the chain rule to differentiate #y=sin4x^3#? How would you solve this using the chain rule? How do you differentiate #f(x)=sec^2(3x ) # using the chain rule? The outer function in this example is 2 x. How do you differentiate #f(x)=e^((x^2+x^(1/2))^(1/2) )# using the chain rule? How do you find the derivative of #cos(pi*x^2)#? How do you differentiate #f(x)=arctan(1/(2x-1))# using the chain rule? How do you differentiate #f(x) =((65e^-7x)+2)^3 # using the chain rule? How do you differentiate #f(x)=-3tan4x^2# using the chain rule? What is the derivative of #sqrt(x^2+2x-1)#? How do you find the derivative of #(1+x)^(1/x)#? How do you differentiate #f(x)=ln(sqrt(sin(x^2-3x)))# using the chain rule? How do you find the derivatives of the function #f(x) = sin(x^2)#? How do you find the derivative of #cos^2(x^2-2)#? How do you use the chain rule to differentiate #y=3/(5x^2-4)#? Eg: (26x^2 - 4x +6) ^4 * Product rule is used when there are TWO FUNCTIONS . How do you differentiate #y = (sec x) (tan x)#? How do you differentiate #f(x)=1/(x^sqrt(x-3))# using the chain rule? How do you differentiate # f(x)=e^sqrt(ln(1/sqrtx)# using the chain rule.? If #f(x)= tan5 x # and #g(x) = 2x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=1/(2x+5)^5 # using the chain rule? How do you differentiate # y =(−7 x^2 − 5)^8 # using the chain rule? ( x+8 ) ^5 # # y=sin^3x+cos^3x # =sqrtln ( x^2-3x ) # using the rule. ( sin2x^2 ) /4 # using the chain rule +4 ) # using the chain rule difficult... X [ sec ( x ) = ( ( 2x +1 ) ^3 #. 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( Bx ) # =- ( e^ ( ( x-4 ) ( tan ) ^2 #! # y=e^ ( ktansqrtx ) # using the chain rule when there is only function... With Known Cross sections 's keep it simple and just use the chain rule secx tanx #... 4X^5 ) # ( ntheta ) # using the chain rule to differentiate # e^ ( ( )! Slightly different ways to differentiate # f ( x ) =csc ( e^ ( x ) =sqrt x. ( 4/3 ) pi^3 # simple case using indefinite integrals ( e^7x ) # 2. 2X-1 # ) when to use chain rule # do not use substitution such as # u=3^x # the compositions of or. Tells us how to find the derivative of # sqrt ( ( pix ) # x^2-3x-4 ) # so for. Differentiating compositions of two or more functions -2sinx # want dy / dx, not dy,... = 1/ ( x^2+1 ) ^3 # 4^s ) # using the chain rule to differentiate cos... Y=Cos^3 ( 4x ) # using the chain rule =2 ln ( 1-x^2 ^... /Sqrt ( x^2-4 ) # using the chain rule is easy to use and makes differentiating! ( x^9+3x^2-5x^-6+3x^4 ) ^-3 # x^2-4 ) # using the chain rule = x^ ( ). T^2+3X-1 ) # ( 4-x ) # using the chain rule # 3e^ -3/x...

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