How do you use the product rule to differentiate #f(x)=(x^2-3x+1)(3x+2)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Andrea S. Nov 28, 2016 The product rule states that: #(d(g(x)*h(x)))/dx = (dg(x))/dx*h(x) + g(x)*(dh(x))/dx# Explanation: Pose: #g(x) = (x^2-3x+1) and h(x) =3x+2# #(df(x))/dx = (d(x^2-3x+1))/dx*(3x+2)+(x^2-3x+1)*(d(3x+2))/dx = (2x-3)(3x+2)+3(x^2-3x+1) = # # = 6x^2+4x-9x-6+3x^2-9x+3= 9x^2-14x-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 1718 views around the world You can reuse this answer Creative Commons License