Derive $\frac{d}{dx} \left[\sin^{-1} x\right] = \frac{1}{\sqrt{1-x^2}}$ (Hint: set $x = \sin y$ and use implicit differentiation)
So, I tried to use the hint and I got:
$x = \sin y$
$\frac{d}{dx}\left[x\right] = \sin y\frac{d}{dx}$
$\frac{dx}{dx} = \cos y \frac{dy}{dx}$
$\frac{dy}{dx} = \frac{1}{\cos y}$
$\frac{dy}{dx} = \sec y$
From here I need a little help.
- Did I do the implicit differentiation correctly?
- How do I use this to help with the original question?