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

Dec 30, 2015

$\cos \frac{t}{{e}^{t} - 1}$

#### Explanation:

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

The derivative of the parametric equation is

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