Answer
$$ y'= -\frac{e^{\cos^{-1}x}}{\sqrt{1-x^2}}.$$
Work Step by Step
Since $ y=e^{\cos^{-1}x}$, then the derivative $ y'$ is given by
$$ y'=e^{\cos^{-1}x} (\cos^{-1}x)'=e^{\cos^{-1}x} \left(-\frac{1}{\sqrt{1-x^2}}\right)=-\frac{e^{\cos^{-1}x}}{\sqrt{1-x^2}}.$$
