How do you differentiate #f(x)=2x(x^2-1)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Jothi S. Dec 6, 2015 2(3x^2-1) Explanation: #f(x)=2x(x^2-1)# #df/dx=2(dx/dx.(x^2-1)+xd/dx(x^2-1))# Product rule: #d/dx(uv)=(du/dx)v+u(dv/dx)# #df/dx=2((x^2-1)+x.2x)# #df/dx=2(x^2-1+2x^2)=2(3x^2-1)# 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 2035 views around the world You can reuse this answer Creative Commons License