Question

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

Answer 1

I found: `g'(x)=36x^2-40x+15`

Explanation:

We derive the first bracket and multiply by the second as it is and add to the product between the first as it is times the derivative of the second (I write in red the derived parts):

`g'(x)=color(red)(8x)(3x-5)+(4x^2+5)color(red)(3)=24x^2-40x+12x^2+15=`
`=36x^2-40x+15`