How do you differentiate #y = (2x^2 + x)(x − x^2)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Shwetank Mauria May 5, 2016 #dy/dx=-8x^3+3x^2+2x# Explanation: Product rule states #d/dxf(x)*g(x)=f(x)*dg(x)/dx+df(x)/dx*g(x)# Differentiating #y=(2x^2+x)(x-x^2)# using product rule #dy/dx=(4x+1)(x-x^2)+(2x^2+x)(1-2x)# or #dy/dx=4x^2-4x^3+x-x^2+2x^2+x-4x^3-2x^2# or #dy/dx=-8x^3+3x^2+2x# 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 1106 views around the world You can reuse this answer Creative Commons License