What is the derivative of # f(x)=e^cosx + cos(e^x)#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Trevor Ryan. Oct 29, 2015 #-sinx*e^(cosx)-e^x*sin(e^x)# Explanation: #d/dx[e^(cosx)+cos(e^x)]=-sinx*e^(cosx)-e^x*sin(e^x)# 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 1587 views around the world You can reuse this answer Creative Commons License