## Task Condition

Find the derivative.

$$
y=\frac{\sqrt[5]{\operatorname{ctg} 2} \cdot \cos ^{2} 18 x}{36 \sin 36 x}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{\sqrt[5]{\operatorname{ctg} 2} \cdot \cos ^{2} 18 x}{36 \sin 36 x}\right)^{\prime}=\frac{\sqrt[5]{\operatorname{ctg} 2}}{36} \cdot\left(\frac{\cos ^{2} 18 x}{\sin 36 x}\right)^{\prime}= \\
& =\frac{\sqrt[5]{\operatorname{ctg} 2}}{36} \cdot\left(\frac{\cos ^{2} 18 x}{2 \sin 18 x \cdot \cos 18 x}\right)^{\prime}=\frac{\sqrt[5]{\operatorname{ctg} 2}}{72} \cdot\left(\frac{\cos 18 x}{\sin 18 x}\right)^{\prime}= \\
& =\frac{\sqrt[5]{\operatorname{ctg} 2}}{72} \cdot(\operatorname{ctg} 18 x)^{\prime}=\frac{\sqrt[5]{\operatorname{ctg} 2}}{72} \cdot \frac{-1}{\sin ^{2} 18 x} \cdot 18=-\frac{\sqrt[5]{\operatorname{ctg} 2}}{4 \sin ^{2} 18 x}
\end{aligned}
$$

Problem Kuznetsov Differentiation 9-18