# What is the derivative of f(t) = (t-lnt, tsint ) ?

$f ' \left(t\right) = \left(1 - \frac{1}{t} , t \cos t + \sin t\right)$
$\frac{\mathrm{df}}{\mathrm{dt}} = \left(1 - \frac{1}{t} , t \cos t + \sin t\right)$