## Condition of the problem

Find the derivative.

$$
y=\cos (\operatorname{ctg} 2)-\frac{1}{16} \cdot \frac{\cos ^{2} 8 x}{\sin 16 x}
$$
## Solution

$y^{\prime}=\left(\cos (\operatorname{ctg} 2)-\frac{1}{16} \cdot \frac{\cos ^{2} 8 x}{\sin 16 x}\right)^{\prime}=-\frac{1}{16} \cdot\left(\frac{\cos ^{2} 8 x}{\sin 16 x}\right)^{\prime}=-\frac{1}{16} \cdot\left(\frac{\cos ^{2} 8 x}{2 \sin 8 x \cdot \cos 8 x}\right)^{\prime}=$ $=-\frac{1}{32} \cdot\left(\frac{\cos 8 x}{\sin 8 x}\right)^{\prime}=-\frac{1}{32} \cdot(\operatorname{ctg} 8 x)^{\prime}=-\frac{1}{32} \cdot \frac{-1}{\sin ^{2} 8 x} \cdot 8=\frac{1}{4 \sin ^{2} 8 x}$

## Problem Kuznetsov Differentiation 9-8