# What is the derivative of f(t) = (lnt, 3t^2+5t ) ?

$f ' \left(t\right) = \left(\frac{1}{t} , 6 t + 5\right)$
Differentiating each component individually with respect to $t$ we get :
$\frac{\mathrm{df}}{\mathrm{dt}} = \left(\frac{1}{t} , 6 t + 5\right)$