How do you differentiate g(x) =sin(3-2x) cos(5x)  using the product rule?

$g ' \left(x\right) = - 2 \cdot \cos \left(3 - 2 x\right) \cdot \cos 5 x - 5 \sin \left(3 - 2 x\right) \cdot \sin 5 x$

Explanation:

from the given
$g \left(x\right) = \sin \left(3 - 2 x\right) \cos 5 x$

Let $u = \sin \left(3 - 2 x\right)$ and let $v = \cos 5 x$

use the formula

$\frac{d}{\mathrm{dx}} \left(u v\right) = u \frac{\mathrm{dv}}{\mathrm{dx}} + v \frac{\mathrm{du}}{\mathrm{dx}}$