# What is the derivative of f(t) = (t^2+1 , e^(1-t) ) ?

Dec 30, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{{e}^{1 - t}}{2 t}$

#### Explanation:

$x ' \left(t\right) = 2 t$
$y ' \left(t\right) = - {e}^{1 - t}$

The derivative of the parametric function is

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y ' \left(t\right)}{x ' \left(t\right)} = - \frac{{e}^{1 - t}}{2 t}$