How do you calculate the derivative of the function #f(x)=e^x(x^2 + 1)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Massimiliano Feb 25, 2015 The answer is: #y'=e^x(x^2+1)+e^x*2x=e^x(x^2+1+2x)=e^x(x+1)^2# This is because the rule says: #y=f(x)rArry'=f'(x)*g(x)+f(x)g'(x)#. 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 9144 views around the world You can reuse this answer Creative Commons License