## Problem Statement

Find the derivative.

$y=\ln \frac{a^{2}+x^{2}}{a^{2}-x^{2}}$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\ln \frac{a^{2}+x^{2}}{a^{2}-x^{2}}\right)^{\prime}=\frac{a^{2}-x^{2}}{a^{2}+x^{2}} \cdot \frac{2 x\left(a^{2}-x^{2}\right)-\left(a^{2}+x^{2}\right) \cdot(-2 x)}{\left(a^{2}-x^{2}\right)^{2}}= \\
& =\frac{2 x\left(a^{2}-x^{2}+a^{2}+x^{2}\right)}{a^{4}-x^{4}}=\frac{4 a^{2} x}{a^{4}-x^{4}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 8-6