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

Dec 30, 2015

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

#### Explanation:

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

The derivative of the parametric equation is

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