If #f(x)= sin3x # and #g(x) = 2x^2 #, how do you differentiate #f(g(x)) # using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Bdub Apr 11, 2016 #[f(g(x))]'=12x cos(6x^2)# Explanation: #f(g(x))=sin(3(2x^2) )= sin(6x^2)# #[f(g(x))]'=f'(g(x))g'(x)# #=cos(6x^2)*12x# #=12x cos(6x^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 1203 views around the world You can reuse this answer Creative Commons License