What is the derivative of e^cosx + cos(e^x)? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Sasha P. Oct 31, 2015 f' = -e^(cosx)sinx-e^xsine^x Explanation: f'=(e^(cosx)+cose^x)' = e^(cosx)(-sinx)-sine^x* e^x f' = -e^(cosx)sinx-e^xsine^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 4976 views around the world You can reuse this answer Creative Commons License