How do you find the derivative of #y = x^4(2x - 5)^6#? Calculus Basic Differentiation Rules Product Rule 1 Answer Henry W. Oct 8, 2016 #y'=u'v+v'u#- product rule Explanation: Let #u=x^4# and #v=(2x-5)^6# #u'=4x^3# #v'=2*6(2x-5)^5=12(2x-5)^5->#by chain rule Subbing into #y'=u'v+v'u#, #y'=4x^3(2x-5)^6+12(2x-5)^5x^4# Simplifying, #y'=x^3(2x-5)^5(4(2x-5)+12x)=x^3(2x-5)^5(20x-20)# 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 3706 views around the world You can reuse this answer Creative Commons License