How do you find the derivative of #e^(x^2)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Base e 1 Answer Alan N. May 13, 2018 #2xe^(x^2)# Explanation: #f(x) = e^(x^2)# Apply chain rule and standard differential. #f'(x) = e^(x^2) * d/dx(x^2)# #= e^(x^2) * 2x# # = 2xe^(x^2)# 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 57402 views around the world You can reuse this answer Creative Commons License