How do you find the derivative of #f(x)= (x^3)(e^(2x))#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Base e 1 Answer Carl S. Mar 31, 2018 #dy/dx = x^2e^{2x}(3+2x)# Explanation: Product rule #d/dx[uv] = {du}/dx v + {dv}/dx u# #u=x^3# #v=e^{2x}# #dy/dx = d/dx[x^3]e^{2x}+d/dx[e^{2x}]x^3# #dy/dx = 3x^2e^{2x}+2e^{2x}x^3# #dy/dx = x^2e^{2x}(3+2x)# 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 5383 views around the world You can reuse this answer Creative Commons License