## Task Condition

Find the derivative.

$$
y=\frac{1}{2} \cdot \operatorname{arctan} \frac{e^{x}-3}{2}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{1}{2} \cdot \operatorname{arctg} \frac{e^{x}-3}{2}\right)^{\prime}=\frac{1}{2} \cdot \frac{1}{1+\left(\frac{e^{x}-3}{2}\right)^{2}} \cdot \frac{e^{x}}{2}= \\
& =\frac{e^{x}}{4} \cdot \frac{4}{4+\left(e^{x}-3\right)^{2}}=\frac{e^{x}}{4+e^{2 x}-6 e^{x}+9}=\frac{e^{x}}{e^{2 x}-6 e^{x}+13}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 7-3