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 1767 views around the world You can reuse this answer Creative Commons License