I was asked to find the derivative of the function
$$
\sin^{-1}(e^x + 3).
$$
First I was thinking of the chain rule, but something looked strange about the function. The domain of $\sin^{-1}$ is $[-1,1]$ and $e^x + 3$ is always strictly greater than $3$. I think that there is a mistake in the problem, but assuming that there isn't: **what exactly is the derivative of a function like this one that "doesn't exist"?** (Is it true to say that the function doesn't exist?)