Chapter 10 - Parametric Equations and Polar Coordinates - 10.2 Calculus with Parametric Curves - 10.2 Exercises - Page 695: 2

$\frac{dy}{dx} = \frac{1 + cos (t)}{(1+t) * e^t}$

We differentiate the x equation using the product rule and get $\frac{dx}{dt} = (t)' * e^t + t * (e^t)' = 1 * e^t + t * e^t = (1+t) * e^t$ We differentiate the y equation and get $\frac{dy}{dt} = 1 + cos(t) $ To get $\frac{dy}{dx} $, we take $\frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{1 + cos(t)}{(1+t) * e^t} $