# What is the derivative of f(t) = (tsint , t^2-tcost ) ?

$f ' \left(t\right) = \left(\begin{matrix}t \sin t ' \\ {t}^{2} ' \\ - t \cos t '\end{matrix}\right) = \left(\sin t + t \cos t , 2 t , - \cos t + t \sin t\right)$
Also, $\left({t}^{n}\right) ' = n {t}^{n - 1} , \left(\sin t\right) ' = \cos t \mathmr{and} \left(\cos t\right) ' = - \sin t$.