## Task Condition

Find the derivative.

$$
y=-\frac{1}{2} \cdot e^{-x^{2}}\left(x^{4}+2 x^{2}+2\right)
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(-\frac{1}{2} \cdot e^{-x^{2}}\left(x^{4}+2 x^{2}+2\right)\right)^{\prime}= \\
& =-\frac{1}{2} \cdot\left(e^{-x^{2}} \cdot(-2 x) \cdot\left(x^{4}+2 x^{2}+2\right)+e^{-x^{2}}\left(4 x^{3}+4 x\right)\right)= \\
& =e^{-x^{2}} \cdot x \cdot\left(x^{4}+2 x^{2}+2\right)-e^{-x^{2}}\left(2 x^{3}+2 x\right)= \\
& =e^{-x^{2}} \cdot\left(x^{5}+2 x^{3}+2 x-2 x^{3}-2 x\right)=x^{5} \cdot e^{-x^{2}}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 7-30