How do you differentiate #f(x)=sqrt(sin(1/(x-2)^2)# using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer maganbhai P. Apr 10, 2018 #I=-1/(x-3)^3xxcos(1/(x-2)^2)/sqrtsin(1/(x-2)^2)# Explanation: Here, #f(x)=sqrt(sin(1/((x-2)^2))# #"Using "color(blue) "Chain Rule"# #f'(x)=1/(2sqrtsin(1/(x-2)^2))d/(dx)(sin(1/(x-2)^2))# #=1/(2sqrtsin(1/(x-2)^2))xxcos(1/(x-2)^2)d/(dx)((x-2)^-2)# #=1/(cancel2sqrtsin(1/(x-2)^2))xxcos(1/(x-2)^2)[-cancel2(x- 2)^-3]# #=-1/(x-3)^3xxcos(1/(x-2)^2)/sqrtsin(1/(x-2)^2)# Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #y=ln(sin(x))# ? How do you find the derivative of #y=ln(e^x+3)# ? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of #y= (4x-x^2)^10# ? How do you find the derivative of #y= (x^2+3x+5)^(1/4)# ? How do you find the derivative of #y= ((1+x)/(1-x))^3# ? See all questions in Chain Rule Impact of this question 1241 views around the world You can reuse this answer Creative Commons License