# How do you differentiate the following parametric equation:  x(t)=-3e^t-2t, y(t)= -5t^2-e^(4t) ?

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{10 t + 4 {e}^{4 t}}{3 {e}^{t} + 2}$
Solve $\frac{\mathrm{dy}}{\mathrm{dt}}$ and $\frac{\mathrm{dx}}{\mathrm{dt}}$
after which divide $\frac{\mathrm{dy}}{\mathrm{dt}}$ by $\frac{\mathrm{dx}}{\mathrm{dt}}$ to obtain $\frac{\mathrm{dy}}{\mathrm{dx}}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$