## Condition of the problem

Find the derivative.

$$
y=\sqrt[3]{\cos \sqrt{2}}-\frac{1}{52} \cdot \frac{\cos ^{2} 26 x}{\sin 52 x}
$$
## Solution

$y^{\prime}=\left(\sqrt[3]{\cos \sqrt{2}}-\frac{1}{52} \cdot \frac{\cos ^{2} 26 x}{\sin 52 x}\right)^{\prime}=0-\frac{1}{52}\left(\frac{\cos ^{2} 26 x}{\sin 52 x}\right)^{\prime}=$

$=-\frac{1}{52} \cdot \frac{\left(\cos ^{2} 26 x\right)^{\prime} \cdot \sin 52 x-\cos ^{2} 26 x \cdot(\sin 52 x)^{\prime}}{\sin ^{2} 52 x}=$

$=-\frac{1}{52} \cdot \frac{2 \cos 26 x \cdot(-\sin 26 x) \cdot 26 \cdot \sin 52 x-\cos ^{2} 26 x \cdot \cos 52 x \cdot 52}{\sin ^{2} 52 x}=$

$=\frac{\cos 26 x \cdot \sin 26 x \cdot \sin 52 x+\cos ^{2} 26 x \cdot \cos 52 x}{\sin ^{2} 52 x}=$

$=\frac{2 \cos ^{2} 26 x \cdot \sin ^{2} 26 x+\cos ^{2} 26 x \cdot\left(1-2 \sin ^{2} 26 x\right)}{\sin ^{2} 52 x}=$

$$
\begin{aligned}
& =\frac{\cos ^{2} 26 x \cdot\left(2 \sin ^{2} 26 x+1-2 \sin ^{2} 26 x\right)}{\sin ^{2} 52 x}=\frac{\cos ^{2} 26 x}{2 \sin ^{2} 26 x \cos ^{2} 26 x}= \\
& =\frac{1}{2 \sin ^{2} 26 x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 9-26