Example 2. Find the derivative of the function $y=\sqrt{1-x^{2}} \arccos x$.
Solution. Differentiating using formulas (2.4) and (2.17), we find

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