## Problem Statement

Find the derivative.

$$
y=\frac{x^{3}}{3} \cdot \arccos x-\frac{2+x^{2}}{9} \cdot \sqrt{1-x^{2}}
$$
## Solution

$y^{\prime}=\left(\frac{x^{3}}{3} \cdot \arccos x-\frac{2+x^{2}}{9} \cdot \sqrt{1-x^{2}}\right)^{\prime}=$
$=x^{2} \cdot \arccos x+\frac{x^{3}}{3} \cdot \frac{-1}{\sqrt{1-x^{2}}}-\frac{2 x}{9} \cdot \sqrt{1-x^{2}}-\frac{2+x^{2}}{9} \cdot \frac{1}{2 \sqrt{1-x^{2}}} \cdot(-2 x)=$ $=x^{2} \cdot \arccos x-\frac{3 x^{3}}{9 \sqrt{1-x^{2}}}-\frac{2 x\left(1-x^{2}\right)}{9 \sqrt{1-x^{2}}}+\frac{x\left(2+x^{2}\right)}{9 \sqrt{1-x^{2}}}=$

$=x^{2} \cdot \arccos x+\frac{-3 x^{3}-2 x+2 x^{3}+2 x+x^{3}}{9 \sqrt{1-x^{2}}}=x^{2} \cdot \arccos x$

## Problem Kuznetsov Differentiation 10-10