Calculus

# Differentiation of Inverse Functions

Given the function $f(x)=3x^2+2x+1$ defined only for $x > 0,$ what is the value of $\left(f^{-1}\right)'(6)?$

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 $\left(f^{-1}\right)'(6)?$

Let $f(x)$ be a differentiable function and let $g(x)$ be the inverse of $f(x)$. If $f(2)=6$ and $f'(2)=\frac{1}{5},$ what is the value of $g'(6)?$

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