## Task Condition

Find the $n$-th order derivative.

$y=3^{2 x+5}$
## Solution

$y^{\prime}=\left(3^{2 x+5}\right)^{\prime}=3^{2 x+5} \cdot \ln 3 \cdot 2$

$y^{\prime \prime}=\left(y^{\prime}\right)^{\prime}=\left(3^{2 x+5} \cdot \ln 3 \cdot 2\right)^{\prime}=3^{2 x+5} \cdot \ln ^{2} 3 \cdot 2^{2}$

...

Obviously,

$y^{(n)}=3^{2 x+5} \cdot \ln ^{n} 3 \cdot 2^{n}=2^{n} \cdot \ln ^{n} 3 \cdot 3^{2 x+5}$

Kuznetsov Differentiation 18-31