Calculus
# Differentiation Rules

Given $\frac{d}{dx} \ln \frac{x+2}{\sqrt{x-7}}=\frac{f(x)}{2(x+2)(x-7)},$ what is $f(x)?$

Given $g(x)=x \sin^{-1} \left(\frac{x}{24}\right)+\sqrt{576-x^2},$ what is the value of $g'(12)$?