How do you find the derivative for #(3x+1)^4(2x-3)^3#? Calculus Basic Differentiation Rules Product Rule 1 Answer Sasha P. Oct 22, 2015 #f'(x)=6(3x+1)^3(2x-3)^2 (6x-5)# Explanation: #f'(x)=((3x+1)^4)' * (2x-3)^3+(3x+1)^4 * ((2x-3)^3)'# #f'(x)=4(3x+1)^3 * 3 * (2x-3)^3+(3x+1)^4 * 3 * (2x-3)^2 * 2# #f'(x)=(3x+1)^3(2x-3)^2 (12(2x-3)+6(3x+1))# #f'(x)=(3x+1)^3(2x-3)^2 (42x-30)# #f'(x)=6(3x+1)^3(2x-3)^2 (6x-5)# 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 3034 views around the world You can reuse this answer Creative Commons License