How do you differentiate #f(x)=cos(xe^(x) ) # using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer A. S. Adikesavan Apr 11, 2016 #f'(x)=-( 1 + x ) e^x sin (xe^x)# Explanation: Using product rule #(xe^x)' =x(e^x)'+e^x(x)' =xe^x+e^x =( 1 + x )e^x#. Using chain rule, #(cos(xe(x))'=-sin(xe^x) (xe^x)'=- sin (xe^x)( 1 + x ) e^x# 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 5237 views around the world You can reuse this answer Creative Commons License