# How do you find the derivative of f(t)=(3^(2t))/t?

$f ' \left(t\right) = \frac{{3}^{2 t} \left(2 \cdot \ln \left(3\right) \cdot t - 1\right)}{t} ^ 2$
$f ' \left(t\right) = \frac{t \cdot \frac{d}{\mathrm{dt}} \left({3}^{2 t}\right) - {3}^{2 t} \cdot \frac{d}{\mathrm{dt}} \left(t\right)}{t} ^ 2$ quotient rule
$f ' \left(t\right) = \frac{t \cdot {3}^{2 t} \cdot \ln \left(3\right) \cdot \frac{d}{\mathrm{dt}} \left(2 t\right) - {3}^{2 t} \cdot 1}{t} ^ 2$ exponent differentiation, chain rule
$f ' \left(t\right) = \frac{t \cdot {3}^{2 t} \cdot \ln \left(3\right) \cdot 2 - {3}^{2 t}}{t} ^ 2$
$f ' \left(t\right) = \frac{{3}^{2 t} \left(2 \cdot \ln \left(3\right) \cdot t - 1\right)}{t} ^ 2$