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

Oct 30, 2017

dy/dx = (e^t-cost)/(e^tcost - e^tsint -1 in terms of $t$

#### Explanation:

We can compute this via noting how;

$\frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$= $\frac{\mathrm{dy}}{\mathrm{dx}}$

Hence $\frac{\mathrm{dy}}{\mathrm{dx}}$ = $\frac{y ' \left(t\right)}{x ' \left(t\right)}$

Hence $x ' \left(t\right) = \frac{\mathrm{dx}}{\mathrm{dt}} = {e}^{t} \cos t - {e}^{t} \sin t - 1$ by considering chain rule and product rule

and $y ' \left(t\right) = \frac{\mathrm{dy}}{\mathrm{dt}} = {e}^{t} - \cos t$

Hence yielding;

(y'(t))/(x'(t)) = dy/dx = (e^t-cost)/(e^tcost - e^tsint -1 in terms of $t$