# How do you differentiate f(x)= 2^(3x)?

Oct 14, 2015

${f}^{'} \left(x\right) = 3 \ln \left(2\right) {2}^{3 x}$

#### Explanation:

First we put this in terms of the base $e$ exponential

$f \left(x\right) = {e}^{3 \ln \left(2\right) x}$

We know that $\frac{d}{\mathrm{dx}} \left({e}^{k x}\right) = k {e}^{k x}$, so for $k = 3 \ln \left(2\right)$ we have

${f}^{'} \left(x\right) = 3 \ln \left(2\right) {2}^{3 x}$