Question #9e2ee Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Base e 1 Answer GiĆ³ Feb 26, 2015 You get: #y'=1*e^(2x)+x*2e^(2x)=e^(2x)+2xe^(2x)=e^(2x)(2x+1)# #y''=2e^(2x)(2x+1)+e^(2x)*2=4xe^(2x)+2e^(2x)+2e^(2x)=# #=4xe^(2x)+4e^(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 5151 views around the world You can reuse this answer Creative Commons License