How do you find the derivative of #f(x)=x^3(x^3-5x+10)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Ratnaker Mehta Jun 22, 2017 # f'(x)=2x^2(3x^3-10x+15).# Explanation: #f(x)=x^3(x^3-5x+10)=x^6-5x^4+10x^3.# Knowing that, #(x^n)'=n*x^(n-1),# we have, #f'(x)=(x^6)'-(5x^4)'+(10x^3#)'# #=6*x^(6-1)-5(x^4)'+10(x^3)'# #=6x^5-5(4x^3)+10(3x^2)# # rArr f'(x)=6x^5-20x^3+30x^2=2x^2(3x^3-10x+15).# 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 1685 views around the world You can reuse this answer Creative Commons License