## problem statement

Find the differential $d y$.

$y=e^{x}(\cos 2 x+2 \sin 2 x)$
## Solution

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

## Problem Kuznetsov Differentiation 4-24