How do you differentiate # y=sin(x^2)(cos(x^2)# using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Shwetank Mauria Jun 18, 2016 #(dy)/(dx)=2xcos(2x^2)# Explanation: #y=sin(x^2)cos(x^2)# = #1/2xx2sin(x^2)cos(x^2)# = #1/2sin(2x^2)# Hence, using chain rule #(dy)/(dx)=1/2xxcos(2x^2)xx4x# = #2xcos(2x^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 1872 views around the world You can reuse this answer Creative Commons License