How do you differentiate #f(x)=(x^2+x)(x^3-1)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer ali ergin May 26, 2016 #d f(x)=(5x^4+4x^3-2x-1)*d x# Explanation: #f(x)=(x^2+x)(x^3-1)# #d f(x)=((x^2+x)^' * (x^3-1)+(x^3-1)^' *(x^2+x))d x# #d f(x)=[(2x+1)(x^3-1)+3x^2(x^2+x)]* d x# #d f(x)=[2x^4-2x+x^3-1+3x^4+3x^3]*d x# #d f(x)=(5x^4+4x^3-2x-1)*d 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 1259 views around the world You can reuse this answer Creative Commons License