If x and y are connected parametrically by the equations given, without eliminating the parameter, Find `(dy)/(dx)`.
`x=a(costheta+thetasintheta), y=a(sintheta-thetacostheta)`

Explanation

To find \(\frac{dy}{dx}\) given the parametric equations \(x = a(\cos \theta + \theta \sin \theta)\) and \(y = a(\sin \theta - \theta \cos \theta)\), we will use the chain rule for derivatives. Specifically, we will compute \(\frac{dy}{d\theta}\) and \(\frac{dx}{d\theta}\), and then use the formula:

\[ \frac{dy}{dx} = \frac{dy/d\theta}{dx/d\theta} \]

### Step 1: Differentiate \(y\) with respect to \(\theta\)

...