How do you differentiate #f(x) = e^(e^x)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Sasha P. Mar 15, 2016 #f'(x) = e^(x+e^x)# Explanation: #f(x) = e^(e^x)# #ln(f(x)) = ln(e^(e^x))# #ln(f(x)) = e^xlne# #ln(f(x)) = e^x# #d/dx(ln(f(x))) = d/dx(e^x)# #1/f(x)*f'(x) = e^x# #f'(x) = e^x * f(x)# #f'(x) = e^x * e^(e^x)# #f'(x) = e^(x+e^x)# Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #y=ln(sin(x))# ? How do you find the derivative of #y=ln(e^x+3)# ? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of #y= (4x-x^2)^10# ? How do you find the derivative of #y= (x^2+3x+5)^(1/4)# ? How do you find the derivative of #y= ((1+x)/(1-x))^3# ? See all questions in Chain Rule Impact of this question 1858 views around the world You can reuse this answer Creative Commons License