How do you differentiate #f(x)= (5+3x^2)*e^x # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer mason m Dec 4, 2015 #f'(x)=e^x(3x^2+6x+5)# Explanation: According to the product rule:: #f'(x)=e^xd/dx[5+3x^2]+(5+3x^2)d/dx[e^x]# #f'(x)=6xe^x+5e^x+3x^2e^x# #f'(x)=e^x(3x^2+6x+5)# Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 1398 views around the world You can reuse this answer Creative Commons License