Question

How do you differentiate `g(u) =(u^-2 + u^3)(u^5 - u^-2)` using the product rule?

Answer 1

• 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`