How do you differentiate #f(x) = x(x^2 - 2x + 1)^4 # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Trevor Ryan. Oct 27, 2015 #d/dxx(x^2-2x+1)^4=(8x^2-8x)(x^2-2x+1)^3+(x^2-2x+1)^4# Explanation: According to the product rule, #d/dx [f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)# #therefored/dxx(x^2-2x+1)^4=(x)*4(x^2-2x+1)^3(2x-2)+(x^2-2x+1)^4# 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 1241 views around the world You can reuse this answer Creative Commons License