Let $f(x)= \sin^{-1}(2e^x)$. What is $f '(\ln(3/10)$? So I tried switching $y= \sin^{-1}(2e^x)$ with $x= \sin(2e^y)$ and then finding the derivative. The answer does not seem to match up. Thanks for the help

It should be $x=\log\left(\frac{1}{2}\sin y\right)$.
$$\sin y = 2e^x\\
\frac{1}{2}\sin y = e^x\\
\log\left(\frac{1}{2}\sin y\right) = x$$
