Derivative of an Inverse Function

Compute $$f'(a)$$ directly, take its reciprocal, substitute back, and simplify

Identify the y-value corresponding to $$a$$, differentiate $$f^{-1}(y)$$ with respect to $$y$$, and then substitute $$y=a$$

Differentiate the inverse function directly using the chain rule, then compute $$f'(a)$$, and take the reciprocal

Identify the x-value where $$f(x)=a$$, compute $$f'(x)$$ at that point, take the reciprocal to obtain $$\left(f^{-1}\right)'(a)$$, and simplify the result