What is the second derivative of #xe^(3x)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Base e 1 Answer Massimiliano Feb 22, 2015 The answer is: #y''=6e^(3x)+9xe^3x# #y'=1*e^(3x)+x*e^(3x)*3=e^(3x)+3xe^(3x)# #y''=e^(3x)*3+3(1*e^(3x)+x*e^(3x)*3)=# #=3e^(3x)+3e^(3x)+9xe^(3x)=6e^(3x)+9xe^3x#. 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 6553 views around the world You can reuse this answer Creative Commons License