Answer
$1$
Work Step by Step
Given
$$y=\int_{0}^{\sin ^{-1} x} \cos t d t$$
Since
\begin{aligned} \frac{dy}{dx}&=\frac{d}{dx}\int_{0}^{\sin ^{-1} x} \cos t d t\\
&= \cos(\sin^{-1}(x))\frac{d}{dx}\sin^{-1}(x)\\
&=\cos(\sin^{-1}(x))\cdot \frac{1}{\sqrt{1-x^2}}\\
&=\sqrt{1-x^2}\cdot \frac{1}{\sqrt{1-x^2}}\\
&=1. \end{aligned}
