How do you differentiate the following parametric equation:  x(t)=t^3-t, y(t)= 1-sint ?

Dec 30, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \frac{t}{1 - 3 {t}^{2}}$

Explanation:

$x ' \left(t\right) = 3 {t}^{2} - 1$
$y ' \left(t\right) = - \cos t$

The derivative of the parametric function is

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y ' \left(t\right)}{x ' \left(t\right)} = \frac{- \cos t}{3 {t}^{2} - 1} = \cos \frac{t}{1 - 3 {t}^{2}}$