## Condition of the problem

Find the differential $d y$

$$
y=2 x+\ln |\sin x+2 \cos x|
$$
## Solution

$$
\begin{aligned}
& d y=y^{\prime} \cdot d x=(2 x-\ln |\sin x+2 \cos x|)^{\prime} d x=\left(2+\frac{1}{\sin x+2 \cos x} \cdot(\cos x-2 \sin x)\right) d x= \\
& =\left(\frac{2 \sin x+1 \cos x+\cos x-2 \sin x}{\sin x+2 \cos x}\right) d x=\frac{5 \cos x}{\sin x+2 \cos x} \cdot d x
\end{aligned}
$$