## Task Condition

Find the derivative.

$$
y=\frac{2}{3} \sqrt{\left(\operatorname{arctan} e^{x}\right)^{3}}
$$
## Solution

$y^{\prime}=\left(\frac{2}{3} \sqrt{\left(\operatorname{arctg} e^{x}\right)^{3}}\right)^{\prime}=\frac{2}{3} \cdot \frac{3}{2} \cdot \sqrt{\operatorname{arctg} e^{x}} \cdot \frac{1}{1+e^{2 x}} \cdot e^{x}=\frac{e^{x} \cdot \sqrt{\operatorname{arctg} e^{x}}}{1+e^{2 x}}$

## Problem Kuznetsov Differentiation 7-6