## Problem Statement

Find the derivative.

$$
y=\frac{1}{m \sqrt{a b}} \operatorname{arctan}\left(e^{m x} \cdot \sqrt{\frac{a}{b}}\right)
$$
## Solution

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

$=\frac{e^{m x}}{b+a \cdot e^{2 m x}}$

## Problem Kuznetsov Differentiation 7-21