# What is the derivative of 5^(3x)?

Mar 2, 2018

$\frac{d}{\mathrm{dx}} \left({a}^{x}\right) = {a}^{x} \ln a$
So, $\frac{d}{\mathrm{dx}} \left({a}^{u}\right) = \left({a}^{u} \ln a\right) \frac{\mathrm{du}}{\mathrm{dx}}$
So $\frac{d}{\mathrm{dx}} \left({5}^{3 x}\right) = \left({5}^{3 x} \ln 5\right) \left(3\right)$
$= 3 \left({5}^{3 x}\right) \ln 5$