# How do you differentiate g(x) = sqrt(x-1)cos(7x) using the product rule?

$f = {\left(x - 1\right)}^{\frac{1}{2}} , g = \cos \left(7 x\right) \to f ' = \frac{1}{2 \sqrt{x - 1}} , g ' = - 7 \sin \left(7 x\right)$
$g ' \left(x\right) = f g ' + g f ' = - 7 \sqrt{x - 1} \sin \left(7 x\right) + \cos \frac{7 x}{2 \sqrt{x - 1}}$