Question

Derivatives of inverse functions
Calculus Help

Answer 1

I presume that I will need to find the inverse. Is that correct?

Answer 2

\[f'(x) = \frac{dy}{dx}\]
\[(f^{-1}(x))' = \frac{dx}{dy} = \frac{1}{dy/dx} = \frac{1}{f'(x)}\]

Answer 3

Sorry my computer is being weird for some reason,
After I do that where do I get the domain from?

Answer 4

Recall that the sine function achieves a maximum value of \(\large\rm 1\),
this happens at an angle of \(\rm \dfrac{\pi}{2}\).

Similarly, the sine function achieves a minimum value of \(\large\rm -1\),
and this occurs at an angle of \(\rm -\dfrac{\pi}{2}\).

In order for the inverse sine to be a `function`,
we have to restrict the domain so that it is one-to-one.