What is the derivative of # f(x)=xcos(cosx))#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Jim S Jun 28, 2018 #f'(x)=cos(cosx)+xsin(cosx)sinx# Explanation: #f(x)=xcos(cosx)# #f'(x)=(xcos(cosx))'=cos(cosx)-xsin(cosx)(cosx)'=cos(cosx)+xsin(cosx)sinx# Answer link Related questions What is the derivative of #y=cos(x)# ? What is the derivative of #y=tan(x)# ? How do you find the 108th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x)# from first principle? How do you find the derivative of #y=cos(x^2)# ? How do you find the derivative of #y=e^x cos(x)# ? How do you find the derivative of #y=x^cos(x)#? How do you find the second derivative of #y=cos(x^2)# ? How do you find the 50th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x^2)# ? See all questions in Derivative Rules for y=cos(x) and y=tan(x) Impact of this question 1730 views around the world You can reuse this answer Creative Commons License