## Task Condition

Find the derivative.

$$
y=\frac{x(\cos (\ln x)+\sin (\ln x))}{2}
$$
## Solution

$y^{\prime}=\left(\frac{x(\cos (\ln x)+\sin (\ln x))}{2}\right)^{\prime}=$

$=\frac{1}{2} \cdot\left(\cos (\ln x)+\sin (\ln x)+x \cdot\left(-\sin (\ln x) \cdot \frac{1}{x}+\cos (\ln x) \cdot \frac{1}{x}\right)\right)=$

$=\frac{1}{2} \cdot(\cos (\ln x)+\sin (\ln x)-\sin (\ln x)+\cos (\ln x))=$

$=\frac{1}{2} \cdot 2 \cos (\ln x)=\cos (\ln x)$

## Problem Kuznetsov Differentiation 8-16