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 2159 views around the world You can reuse this answer Creative Commons License