## Condition of the problem

Find the derivative.

$$
y=\frac{\operatorname{ctg}\left(\sin \frac{1}{3}\right) \cdot \sin ^{2} 17 x}{17 \cos 34 x}
$$
## Solution

$$
\begin{aligned}
& y^{\prime}=\left(\frac{\operatorname{ctg}\left(\sin \frac{1}{3}\right) \cdot \sin ^{2} 17 x}{17 \cos 34 x}\right)^{\prime}= \\
& =\frac{\operatorname{ctg}\left(\sin \frac{1}{3}\right)}{17} \cdot \frac{2 \sin 17 x \cdot \cos 17 x \cdot 17 \cdot \cos 34 x-\sin ^{2} 17 x \cdot(-\sin 34 x) \cdot 34}{\cos ^{2} 34 x}= \\
& =\frac{\operatorname{ctg}\left(\sin \frac{1}{3}\right)}{17} \cdot \frac{17 \sin 34 x \cdot \cos 34 x+34 \sin ^{2} 17 x \cdot \sin 34 x}{\cos ^{2} 34 x}= \\
& =\frac{\operatorname{ctg}\left(\sin \frac{1}{3}\right)}{17} \cdot \frac{17 \sin 34 x \cdot\left(\cos 34 x+34 \sin ^{2} 17 x\right)}{\cos ^{2} 34 x}= \\
& =\frac{\operatorname{ctg}\left(\sin \frac{1}{3}\right)}{17} \cdot \frac{17 \sin 34 x \cdot\left(1-2 \sin ^{2} 17 x+2 \sin ^{2} 17 x\right)}{\cos ^{2} 34 x}= \\
& =\frac{\operatorname{ctg}\left(\sin \frac{1}{3}\right)}{17} \cdot \frac{17 \sin 34 x}{\cos ^{2} 34 x}=\frac{\operatorname{ctg}\left(\sin ^{\frac{1}{3}}\right) \cdot \operatorname{tg} 34 x}{\cos 34 x}
\end{aligned}
$$

## Problem Kuznetsov Differentiation 9-17