How do you differentiate the following parametric equation:  x(t)=tcost, y(t)=tsint ?

Nov 21, 2015

$\alpha ' \left(t\right) = \left(x ' , y '\right) \left(t\right)$

Explanation:

Differentiate $\alpha = \left(x , y\right)$ on $t$.

$x ' = t ' \cos t + t \cos ' t = 1 \cos t + t \left(- \sin t\right)$

$y ' = t ' \sin t + t \sin ' t = 1 \sin t + t \left(\cos t\right)$

$\alpha ' \left(t\right) = \left(\begin{matrix}\cos t - t \sin t \\ \sin t + t \cos t\end{matrix}\right)$