How do you differentiate #g(u) =(u^-2 + u^3)(u^5 - u^-2) # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Guilherme N. Jan 5, 2016 Product rule: #(ab)'=a'b+ab'# Explanation: #(dg(u))/(du)=(-2u^-3+3u^2)(u^5-u^-2)+(u^-2+u^3)(5u^4+2u^-3)# #(dg(u))/(du)=-2u^2+2u^-5+3u^7-3+5u^2+2u^-5+5u^7+2# #(dg(u))/(du)=3u^2+4u^-5+8u^7-1# 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 1673 views around the world You can reuse this answer Creative Commons License