## Task Condition

Find the derivative.

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

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

$=\frac{1}{a^{2}+\beta^{2}}\left(\alpha \cdot e^{a x}(3 \cdot \sin 3 x-\alpha \cos 3 x)+\epsilon^{\alpha x}\left(3^{2} \cdot \cos 3 x+a \cdot 3 \cdot \sin 3 x\right)\right)=$

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

$=\frac{\epsilon^{-\alpha x}\left(3^{2} \cdot \cos 3 x+2 a \beta \sin 3 x-\alpha^{2} \cdot \cos 3 x\right)}{a^{2}+3^{2}}$

Problem Kuznetsov Differentiation 7-12