How do you find the 1st and 2nd derivative of #x^2e^x#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Base e 1 Answer Noah G Nov 14, 2016 #dy/dx = x(x + 2)e^x# #(d^2y)/(dx^2) = (x^2 +4x + 2)e^x# Explanation: By the product rule. #dy/dx = 2x xx e^x + e^x xx x^2# #dy/dx = 2xe^x + x^2e^x# #dy/dx = x(x + 2)e^x# #(d^2y)/(dx^2) = 2 xx e^x + 2x xx e^x + 2x xx e^x + x^2xxe^x# #(d^2y)/(dx^2) = 2e^x + 2xe^x + 2xe^x + x^2e^x# #(d^2y)/(dx^2) = 2e^x + 4xe^x + x^2e^x# #(d^2y)/(dx^2) = (x^2 + 4x +2)e^x# Hopefully this helps! 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 9522 views around the world You can reuse this answer Creative Commons License