Condition of the problem

Find the $n$-th order derivative.

$y=2^{k x}$
## Solution

$y=2^{k x}=\left(e^{\ln 2}\right)^{k x}=e^{k \ln 2 \cdot x}$

$y^{\prime}=\left(e^{k \ln 2 \cdot x}\right)^{\prime}=e^{k \ln 2 \cdot x} \cdot k \ln 2$
$y^{\prime \prime}=\left(y^{\prime}\right)^{\prime}=\left(e^{k \ln 2 \cdot x} \cdot k \ln 2\right)^{\prime}=e^{k \ln 2 \cdot x} \cdot k^{2} \ln ^{2} 2$

$\cdots$

Obviously,

$y^{(n)}=e^{k \ln 2 \cdot x} \cdot k^{n} \ln ^{n} 2=2^{k x} \cdot k^{n} \ln ^{n} 2$

## Problem Kuznetsov Differentiation 18-26