## Condition of the problem

Find the derivative.

$$
y=\operatorname{ctg}(\cos 5)-\frac{1}{40} \cdot \frac{\cos ^{2} 20 x}{\sin 40 x}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\operatorname{ctg}(\cos 5)-\frac{1}{40} \cdot \frac{\cos ^{2} 20 x}{\sin 40 x}\right)^{\prime}= \\
& =0-\frac{1}{40} \cdot\left(\frac{\cos ^{2} 20 x}{\sin 40 x}\right)^{\prime}=-\frac{1}{40} \cdot\left(\frac{\cos ^{2} 20 x}{2 \sin 20 x \cdot \cos 20 x}\right)^{\prime}
\end{aligned}
$$

$$
\begin{aligned}
& =-\frac{1}{80} \cdot\left(\frac{\cos 20 x}{\sin 20 x}\right)^{\prime}=-\frac{1}{80} \cdot(\operatorname{ctg} 20 x)^{\prime}= \\
& =-\frac{1}{80} \cdot \frac{-1}{\sin ^{2} 20 x} \cdot 20=\frac{1}{4 \sin ^{2} 20 x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 9-20