## Task Condition

Find the derivative.

$$
y=\sqrt[3]{\operatorname{ctg} 2}-\frac{1}{20} \cdot \frac{\cos ^{2} 10 x}{\sin 20 x}
$$
## Solution

$y^{\prime}=\left(\sqrt[3]{\operatorname{ctg} 2}-\frac{1}{20} \cdot \frac{\cos ^{2} 10 x}{\sin 20 x}\right)^{\prime}=0-\frac{1}{20} \cdot\left(\frac{\cos ^{2} 10 x}{\sin 20 x}\right)^{\prime}=$

$=-\frac{1}{20} \cdot\left(\frac{\cos ^{2} 10 x}{2 \sin 10 x \cdot \cos 10 x}\right)^{\prime}=-\frac{1}{40} \cdot\left(\frac{\cos 10 x}{\sin 10 x}\right)^{\prime}=$

$=-\frac{1}{40} \cdot(\operatorname{ctg} 10 x)^{\prime}=-\frac{1}{40} \cdot \frac{-1}{\sin ^{2} 10 x} \cdot 10=\frac{1}{4 \sin ^{2} 10 x}$

Problem Kuznetsov Differentiation 9-10