Calculus
# Differentiation Rules

Given the function $f(x)=5\ln\frac{x}{4},$ what is the value of $\left(f^{-1}\right)'(\ln32)?$

If $f(x)=5\sin^{-1}3x,$ what is the value of $f'\left(\frac{\sqrt{3}}{6} \right)?$

Given $f(x)=5x+\frac{1}{x}$ in the domain $x > \frac{1}{2} ,$ what is $\left(f^{-1}\right)'(6)?$