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 4724 views around the world You can reuse this answer Creative Commons License