Answer
$\frac{dy}{dx} = \frac{2t+1}{ t\cos t + \sin t}$
Work Step by Step
We will need to use the following formula:
$$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$$
This formula lets us calculate ${\frac{dy}{dt}}$ and ${\frac{dx}{dt}}$ individually, then take their quotient to obtain $\frac{dy}{dx}$.
$\frac{dy}{dt} = \frac{d}{dt}(t^2+t) = 2t+1$
$\frac{dx}{dt} = \frac{d}{dt}(t\sin t) = t\cos t + \sin t$
$\frac{dy}{dx} = \frac{2t+1}{ t\cos t + \sin t}$
