Question

How to find the derivate of `(x+3)*(x^-2+8)` ?

`(x+3)*(x^-2+8)` ?

Answer 1

`f’(x)=8-x^-2-6x^-3`

Explanation:

`u=x+3`, `du=1`
`v=x^-2+8`,`dv=-2x^-3`
`f’(x)=v.du+u.dv`
`=((x^-2+8).1)+((x+3).(-2x^-3))`
`=x^-2+8-2x^-2-6x^-3=8-x^-2-6x^-3`
`f’(x)=8-(1/x^2)-(6/x^3)=(1/x^3)(8x^3-x-6)`