Question

How do you differentiate `g(y) = (x^2 - 1) (4x^6 + 5)` using the product rule?

Answer 1

`g'(x) = 2x(4x^6 + 5) + 24x^5(x^2 - 1)`

Explanation:

`g` is the product of two functions `u` & `v` with `u(x) = x^2 - 1` & `v(x) = 4x^6 + 5`

So the derivative of `g` is `u'v + uv'` with `u'(x) = 2x` & `v'(x) = 24x^5`.