How do you differentiate #sin(x^4)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer 256 Aug 4, 2017 #4x^3cos(x^4)# Explanation: By the chain rule #(sin(x^4))'=(x^4)'sin'(x^4)# #=4x^3sin'(x^4)# by the power rule And since #sin'(x)=cos(x)# #(sin(x^4))'=4x^3cos(x^4)# 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 8551 views around the world You can reuse this answer Creative Commons License