## Task Condition

Find the derivative.

$y=\ln \cos \frac{1}{3}+\frac{\sin ^{2} 23 x}{23 \cos 46 x}$
## Solution

$y^{\prime}=\left(\ln \cos \frac{1}{3}+\frac{\sin ^{2} 23 x}{23 \cos 46 x}\right)^{\prime}=0+\left(\frac{\sin ^{2} 23 x}{23 \cos 46 x}\right)^{\prime}=$

$=\frac{2 \sin 23 x \cdot \cos 23 x \cdot 23 \cdot \cos 46 x-\sin ^{2} 23 x \cdot(-\sin 46 x) \cdot 46}{23 \cos ^{2} 46 x}=$

$=\frac{\sin 46 x \cdot \cos 46 x+2 \sin ^{2} 23 x \cdot \sin 46 x}{\cos ^{2} 46 x}=$

$=\frac{\sin 46 x \cdot\left(\cos 46 x+2 \sin ^{2} 23 x\right)}{\cos ^{2} 46 x}=\frac{\sin 46 x \cdot\left(1-2 \sin ^{2} 23 x+2 \sin ^{2} 23 x\right)}{\cos ^{2} 46 x}=$

$=\frac{\sin 46 x}{\cos ^{2} 46 x}=\frac{\operatorname{tg} 46 x}{\cos 46 x}$

Kuznetsov Differentiation 9-23