How do you differentiate #F(y)=(1/y^2-3/y^4)(y+5y^3)#? Calculus Basic Differentiation Rules Product Rule 1 Answer HCH Jul 19, 2017 Answer: #d/dyF(y)=15y^2+59/y^2+9/y^4-55# Explanation: #F(y)=(1/y^2-3/y^4)(y+5y^3)# Since, #d/dxg(x)f(x)=g(x)f'(x)+f(x)g'(x)# #d/dyF(y)=(1/y^2-3/y^4)d/dy(y+5y^3)+d/dy(1/y^2-3/y^4)(y+5y^3)# #d/dyF(y)=(1/y^2-3/y^4)(1+15y^4)+(-2/y^3+12/y^5)(y+5y^3)# #d/dyF(y)=(1/y^2-3/y^4-45+15y^2)+(-2/y^2+12/y^4-10+60/y^2)# #d/dyF(y)=1/y^2-3/y^4-45+15y^2-2/y^2+12/y^4-10+60/y^2# #d/dyF(y)=15y^2+59/y^2+9/y^4-55# 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 888 views around the world You can reuse this answer Creative Commons License