I need help with this exercise:
For a suitable branch cuts we have that \begin{align*} \frac{d}{dz}\arcsin(z)=\frac{1}{(1-z^{2})^{1/2}}, \end{align*} for all $z\neq \pm 1$. Investigate the possible branch cuts that makes this formula valid.
Should I look at the branch point? Which should be at $\pm 1$ since the square-root is then $0$. But how should I know the branch cuts?
Or for the formula to be valid do I somehow have look at branch cuts on $\frac{d}{dz}\arcsin(z)$ and compare it to the branch cuts of $\frac{1}{(1-z^{2})^{1/2}}$?
Can someone please help me with this, I am abit lost. Thanks!