Question

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

Answer 1

`g'(y)=12x^3-15x^2+6x-5`

Explanation:

Let `u=(x^3+x)`
`d'u=3x^2+1`

let `v=(3x-5)`
`d'v=3`

`g(y)=uv`
`g'(y)=ud'v+vd'u`
`g'(y)=(x^3+x)(3)+(3x-5)(3x^2+1)`
`g'(y)=3x^3+3x+9x^3+3x-15x^2-5`
`g'(y)=3x^3+9x^3-15x^2+3x+3x-5`
`g'(y)=12x^3-15x^2+6x-5`