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

Mar 1, 2017

$y ' = \frac{\left(- 3 {e}^{t} - 4\right) '}{\left(- 10 t - {e}^{t}\right) '}$

#### Explanation:

The derivative can be found like this:
$y ' = \frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$
Basically, it is the derivatives divided by each other.

$y ' = \frac{\left(- 3 {e}^{t} - 4 t\right) '}{\left(- 5 {t}^{2} - {e}^{t}\right) '}$

$y ' = \frac{\left(- 3 {e}^{t} - 4\right) '}{\left(- 10 t - {e}^{t}\right) '}$

Check out the website for a good explanation (much better than mine)

http://tutorial.math.lamar.edu/Classes/CalcII/ParaTangent.aspx