Question

How do you differentiate `f(x)=(x-3lnx)(cosx+2x)` using the product rule?

Answer 1

We will use the formula:

`y = f (x) cdot g(x) rArr y' = f' (x) cdot g (x) + f (x) cdot g' (x)`.

Explanation:

Detailed operations are as follows:

`f' (x) = (x- 3 ln x)' cdot (cos x + 2 x) + (x - 3 ln x) cdot (cos x + 2 x)'`

`f' (x) = (1 - 3/x) cdot (cos x + 2 x) + (x - 3 ln x) cdot (- sin x + 2)`.

We could try to develop the products but the resulting expression can not be oversimplified and worth writing no more.