## Condition of the problem

Find the derivative.

$$
y=\operatorname{ctg} \sqrt[3]{5}-\frac{1}{8} \cdot \frac{\cos ^{2} 4 x}{\sin 8 x}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\operatorname{ctg} \sqrt[5]{5}-\frac{1}{8} \cdot \frac{\cos ^{2} 4 x}{\sin 8 x}\right)^{\prime}=-\frac{1}{8} \cdot\left(\frac{\cos ^{2} 4 x}{\sin 8 x}\right)^{\prime}=-\frac{1}{8} \cdot\left(\frac{\cos ^{2} 4 x}{2 \sin 4 x \cdot \cos 4 x}\right)^{\prime}= \\
& =-\frac{1}{16} \cdot\left(\frac{\cos 4 x}{\sin 4 x}\right)^{\prime}=-\frac{1}{16} \cdot(\operatorname{ctg} 4 x)^{\prime}=-\frac{1}{16} \cdot \frac{-1}{\sin ^{2} 4 x} \cdot 4=\frac{1}{4 \sin ^{2} 4 x}
\end{aligned}
$$