## Task Condition

Find the derivative.

$y=\ln \left(x+\sqrt{a^{2}+x^{2}}\right)$
## Solution

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

## Problem Kuznetsov Differentiation 8-2