## Task Condition

Find the derivative.

$$
y=\cos ^{2}(\sin 3)+\frac{\sin ^{2} 29 x}{29 \cos 58 x}
$$
## Solution

$y^{\prime}=\left(\cos ^{2}(\sin 3)+\frac{\sin ^{2} 29 x}{29 \cos 58 x}\right)^{\prime}=0+\left(\frac{\sin ^{2} 29 x}{29 \cos 58 x}\right)^{\prime}=$

$=\frac{2 \sin 29 x \cdot \cos 29 x \cdot 29 \cdot \cos 58 x-\sin ^{2} 29 x \cdot(-\sin 58 x) \cdot 58}{29 \cos ^{2} 58 x}=$

$=\frac{\sin 58 x \cdot \cos 58 x+2 \sin ^{2} 29 x \cdot \sin 58 x}{\cos ^{2} 58 x}=\frac{\sin 58 x \cdot\left(\cos 58 x+2 \sin ^{2} 29 x\right)}{\cos ^{2} 58 x}=$

$=\frac{\sin 58 x \cdot\left(1-2 \sin ^{2} 29 x+2 \sin ^{2} 29 x\right)}{\cos ^{2} 58 x}=\frac{\sin 58 x}{\cos ^{2} 58 x}=\frac{\operatorname{tg} 58 x}{\cos 58 x}$

## Problem Kuznetsov Differentiation 9-29