## Task Condition

Find the derivative.

$$
y=\frac{3^{x}(\ln 3 \cdot \sin 2 x-2 \cos 2 x)}{\ln ^{2} 3+4}
$$
## Solution

$y^{\prime}=\left(\frac{3^{x}(\ln 3 \cdot \sin 2 x-2 \cos 2 x)}{\ln ^{2} 3+4}\right)^{\prime}=$

$=\frac{1}{\ln ^{2} 3+4} \cdot\left(3^{x} \cdot \ln 3 \cdot(\ln 3 \cdot \sin 2 x-2 \cos 2 x)+3^{x}(2 \ln 3 \cdot \cos 2 x+4 \sin 2 x)\right)=$

$=\frac{3^{x}}{\ln ^{2} 3+4} \cdot\left(\ln ^{2} 3 \cdot \sin 2 x-2 \ln 3 \cdot \cos 2 x+2 \ln 3 \cdot \cos 2 x+4 \sin 2 x\right)=$

$=\frac{3^{x}}{\ln ^{2} 3+4} \cdot\left(\ln ^{2} 3 \cdot \sin 2 x+4 \sin 2 x\right)=\frac{3^{x} \cdot \sin 2 x}{\ln ^{2} 3+4} \cdot\left(\ln ^{2} 3+4\right)=3^{x} \cdot \sin 2 x$

## Problem Kuznetsov Differentiation 15-29