# How do you differentiate the following parametric equation:  x(t)=-3e^t-2t, y(t)= -5t^2+2 ?

Dec 30, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{10 t}{3 {e}^{t} + 2}$

#### Explanation:

$x ' \left(t\right) = - 3 {e}^{t} - 2$
$y ' \left(t\right) = - 10 t$

The derivative of the parametric function is

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y ' \left(t\right)}{x ' \left(t\right)} = \frac{- 10 t}{- 3 {e}^{t} - 2} = \frac{10 t}{3 {e}^{t} + 2}$