## Task Condition

Find the derivative.

$y=\operatorname{arctg}\left(e^{x}-e^{-x}\right)$
## Solution

$y^{\prime}=\left(\operatorname{arctg}\left(e^{x}-e^{-x}\right)\right)^{\prime}=\frac{1}{1+\left(e^{x}-e^{-x}\right)^{2}} \cdot\left(e^{x}-e^{-x}\right)^{\prime}=$

$$
\begin{aligned}
& =\frac{1}{1+\left(e^{x}-e^{-x}\right)^{2}} \cdot\left(e^{x}+e^{-x}\right)=\frac{e^{x}+e^{-x}}{1+e^{2 x}-2+e^{-2 x}}= \\
& =\frac{e^{x}+e^{-x}}{1+e^{2 x}-2+e^{-2 x}}=\frac{e^{3 x}+e^{x}}{e^{4 x}-e^{2 x}+1}
\end{aligned}
$$

Kuznetsov Differentiation 7-26