# How do you differentiate the following parametric equation:  x(t)=t, y(t)= 1-tcost ?

Dec 30, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = t \sin t - \cos t$

#### Explanation:

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

The derivative of the parametric function is

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y ' \left(t\right)}{x ' \left(t\right)} = \frac{- \cos t + t \sin t}{1} = t \sin t - \cos t$