If f is the inverse of g, then we know that f(g(x))=x, how do you use this fact to derive the derivative formula dy/dx e^x= e^x? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Base e 1 Answer Andrea S. Dec 13, 2016 Pose #f(x) = lnx# and #g(x) = e^x# Explanation: #x=lne^x# #d/(dx) (x) = d/(dx) (lne^x)# #1 = 1/e^x d/(dx)(e^x)# #e^x = d/(dx)(e^x)# Answer link Related questions What is the derivative of #y=3x^2e^(5x)# ? What is the derivative of #y=e^(3-2x)# ? What is the derivative of #f(theta)=e^(sin2theta)# ? What is the derivative of #f(x)=(e^(1/x))/x^2# ? What is the derivative of #f(x)=e^(pix)*cos(6x)# ? What is the derivative of #f(x)=x^4*e^sqrt(x)# ? What is the derivative of #f(x)=e^(-6x)+e# ? How do you find the derivative of #y=e^x#? How do you find the derivative of #y=e^(1/x)#? How do you find the derivative of #y=e^(2x)#? See all questions in Differentiating Exponential Functions with Base e Impact of this question 1405 views around the world You can reuse this answer Creative Commons License