## Task Condition

Find the derivative.

$$
y=x(\arcsin x)^{2}+2 \sqrt{1-x^{2}} \arcsin x-2 x
$$
## Solution

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

$=(\arcsin x)^{2}+x \cdot 2 \cdot \arcsin x \cdot \frac{1}{\sqrt{1-x^{2}}}+\frac{2}{2 \sqrt{1-x^{2}}} \cdot(-2 x) \cdot \arcsin x+2 \sqrt{1-x^{2}} \cdot \frac{1}{\sqrt{1-x^{2}}}-2=$ $=(\arcsin x)^{2}+\frac{2 x \cdot \arcsin x}{\sqrt{1-x^{2}}}-\frac{2 x \cdot \arcsin x}{\sqrt{1-x^{2}}}+2-2=(\arcsin x)^{2}$

## Problem Kuznetsov Differentiation 14-24