Answer
$$\frac{dy}{dx}=\frac{1+\cos t}{(t+1)e^t}$$
Work Step by Step
The formula of the derivative of a parametric equation is;
$$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$$
Finding the derivative of both parameters with respect to $t$, we get:
$$\frac{dy}{dt}=1+\cos t\\\frac{dx}{dt}=e^t+te^t=(1+t)e^t$$
Taking the ratio of the two derivatives to find $dy/dx$, we get:
$$\frac{dy}{dx}=\frac{1+\cos t}{(1+t)e^t}$$
