## Problem Statement

Find the derivative.

$y=\sqrt{1-x^{2}}-x \cdot \arcsin \sqrt{1-x^{2}}$
## Solution

$y^{\prime}=\left(\sqrt{1-x^{2}}-x \cdot \arcsin \sqrt{1-x^{2}}\right)^{\prime}=$

$$
\begin{aligned}
& =\frac{1}{2 \sqrt{1-x^{2}}} \cdot(-2 x)-\left(\arcsin \sqrt{1-x^{2}}+x \cdot \frac{1}{\sqrt{1-\left(\sqrt{1-x^{2}}\right)^{2}}} \cdot \frac{1}{2 \sqrt{1-x^{2}}} \cdot(-2 x)\right)= \\
& =-\frac{x}{\sqrt{1-x^{2}}}-\arcsin \sqrt{1-x^{2}}-\frac{x}{\sqrt{x^{2}}} \cdot \frac{-x}{\sqrt{1-x^{2}}}= \\
& =-\frac{x}{\sqrt{1-x^{2}}}-\arcsin \sqrt{1-x^{2}}+\frac{x}{\sqrt{1-x^{2}}}=-\arcsin \sqrt{1-x^{2}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 10-23