## Task Condition

Find the derivative.

$y=\sin (\ln 2)+\frac{\sin ^{2} 25 x}{25 \cos 50 x}$
$$
\begin{aligned}
& y^{\prime}=\left(\sin (\ln 2)+\frac{\sin ^{2} 25 x}{25 \cos 50 x}\right)^{\prime}=0+\left(\frac{\sin ^{2} 25 x}{25 \cos 50 x}\right)^{\prime}= \\
& =\frac{1}{25}\left(\frac{\sin ^{2} 25 x}{\cos 50 x}\right)^{\prime}=\frac{1}{25}\left(\frac{\left(\sin ^{2} 25 x\right)^{\prime} \cdot \cos 50 x-\sin ^{2} 25 x \cdot(\cos 50 x)^{\prime}}{\cos ^{2} 50 x}\right)= \\
& =\frac{1}{25}\left(\frac{2 \sin 25 x \cdot \cos 25 x \cdot 25 \cdot \cos 50 x-\sin ^{2} 25 x \cdot(-\sin 50 x \cdot 50)}{\cos ^{2} 50 x}\right)= \\
& =\frac{1}{25}\left(\frac{25 \sin 50 x \cdot \cos 50 x+50 \sin ^{2} 25 x \cdot \sin 50 x}{\cos ^{2} 50 x}\right)= \\
& =\frac{1}{25}\left(\frac{25 \sin 50 x\left(\cos 50 x+2 \sin ^{2} 25 x\right)}{\cos ^{2} 50 x}\right)= \\
& =\frac{\sin 50 x\left(1-2 \sin ^{2} 25 x+2 \sin ^{2} 25 x\right)}{\cos ^{2} 50 x}=\frac{\sin 50 x}{\cos ^{2} 50 x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 9-25