differentiation

$\dfrac{d}{dx}\ln (\sin x)\\ u=\sin x\,\,\,\, y=\ln u\\ \dfrac{dy}{dx}=\dfrac{dy}{du}\times \dfrac{du}{dx}=\dfrac{1}{u}\times \cos x=\dfrac{\cos x}{\sin x}=\cot x$

$\therefore f'(x)= \dfrac{d}{dx}(5x^2) + \cot x = 10x + \cot x$

What's f'(x)?