How do you differentiate # f(x)=(6x-4)(6x+1)^3 # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Leland Adriano Alejandro Jan 10, 2016 #f' (x) = 6(6x+1)^2 (24x-11)# Explanation: start with the given #f (x) =(6x-4)(6x+1)^3# #f' (x) = (6x-4)*3(6x+1)^3*6+(6x+1)^3*6# #f' (x)=6(6x+1)^2 (3*(6x-4)+6x+1)# #f' (x)=6(6x+1)^2(18x-12+6x+1)# #f' (x)=6(6x+1)^2(24x-11)# 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 1315 views around the world You can reuse this answer Creative Commons License