How do you find the derivative of #(2x)/(3+e^x)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Base e 1 Answer Jake M. Mar 7, 2018 #(6+2e^x - 2xe^x)/(3+e^x)^2 # Explanation: We can use quotient rule: #d/dx(f/g) = (gf' - fg')/g^2 # If #f(x) = 2x# and #g(x) = 3 + e^x#, the derivative is #(2(3+e^x) - 2x(e^x))/(3+e^x)^2 = (6+2e^x - 2xe^x)/(3+e^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 1853 views around the world You can reuse this answer Creative Commons License