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

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Answer 1 · 2017-03-05T15:53:25

We will use the formula:

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

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.

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