## Task Condition

Find the derivative.

$$
y=\frac{\sin \left(\tan \frac{1}{7}\right) \cdot \cos ^{2} 16 x}{32 \sin 32 x}
$$
## Solution

$y^{\prime}=\left(\frac{\sin \left(\tan \frac{1}{7}\right) \cdot \cos ^{2} 16 x}{32 \sin 32 x}\right)^{\prime}=$

$=\sin \left(\tan \frac{1}{7}\right) \cdot\left(\frac{\cos ^{2} 16 x}{64 \sin 16 x \cdot \cos 16 x}\right)^{\prime}=$

$=\frac{\sin \left(\tan \frac{1}{7}\right)}{64} \cdot\left(\frac{\cos 16 x}{\sin 16 x}\right)^{\prime}=\frac{\sin \left(\tan \frac{1}{7}\right)}{64} \cdot(\cot 16 x)^{\prime}=$

$=\frac{\sin \left(\tan \frac{1}{7}\right)}{64} \cdot \frac{-1}{\sin ^{2} 16 x} \cdot 16=-\frac{\sin \left(\tan \frac{1}{7}\right)}{4 \sin ^{2} 16 x}$

Problem Kuznetsov Differentiation 9-16