If #f(x)= x^2-x # and #g(x) = x^( 1/3 ) #, what is #f'(g(x)) #? Calculus Basic Differentiation Rules Chain Rule 1 Answer A. S. Adikesavan Dec 21, 2016 #1/3x^(-1/3)(2-x^(-1/3))# Explanation: #f(g)=g^2-g=(x^(1/3))^2-x^(1/3)=x^(2/3)-x^(1/3)# #f'(g(x)# #= (x^(2/3)-x^(1/3))'# #=2/3x^(-1/3)-1/3x^(-2/3)# #=1/3x^(-1/3)(2-x^(-1/3))# 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 1179 views around the world You can reuse this answer Creative Commons License