Question

How do you differentiate `g(y) =(2x-5 )(x^3 + 4)` using the product rule?

Answer 1

`8x^3-15x^2+8`

Explanation:

Using the product rule

`(uv)'=u'v+uv'`
we get

`g'(x)=2(x^3+4)+(2x-5)3x^2`
expanding we get

`g'(x)=2x^3+8+6x^3-10x^2`
collecting like terms

`g'(x)=8x^3-25x^2+8`