## Task Condition

Find the derivative.

$$
y=\left(1+x^{2}\right) e^{\operatorname{arctg} x}
$$
## Solution

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

## Problem Kuznetsov Differentiation 15-11