How do you differentiate #g(x) = (x^2+1) (x-3)^3# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Lucy Apr 13, 2018 #g'(x) = (x-3)^2(5x^2-6x+3)# Explanation: #g(x) = (x^2+1)(x-3)^3# #g'(x) = (2x)(x-3)^3 + (x^2+1)3(x-3)^2# #g'(x) = (x-3)^2(2x^2-6x+3x^2+3)# #g'(x) = (x-3)^2(5x^2-6x+3)# 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 1228 views around the world You can reuse this answer Creative Commons License