Derivative of the Inverse Sine Function

Implicit differentiation of $y=\sin^{-1}(x)$ leads to the relation $\cos(y)*(dy/dx)=1$, resulting in the correct derivative.

The derivative of $\sin^{-1}(x)$ is $\frac{1}{\sqrt{1-x^2}}$.

The derivative is only defined for $|x| < 1$.

The derivative of $\sin^{-1}(x)$ is $\frac{1}{1-x^2}$.