How do you differentiate #p(y) = (y + ln(y)y^2(5y^3 + 9y^4)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer bp Feb 29, 2016 #1+ln(y) (25y^4 +54y^5) +(5y^4+9y^5)# Explanation: Write# p(y)= y +ln(y) *(5y^5 +9y^6)# #p' (y) = 1 + ln(y) (25y^4+54y^5) +(1/y)(5y^5 +9y^6)# =#1+ln(y) (25y^4 +54y^5) +(5y^4+9y^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 1321 views around the world You can reuse this answer Creative Commons License