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 \(\frac{dy}{dx}\) for the given parametric equations \(x = a(\cos \theta + \theta \sin \theta)\) and \(y = a(\sin \theta - \theta \cos \theta)\), we will use the chain rule. The derivative \(\frac{dy}{dx}\) can be expressed as \(\frac{dy/d\theta}{dx/d\theta}\).

### Step 1: Find \(\frac{dy}{d\theta}\)

Starting with the equation for \(y\):
\[ y = a(\sin \theta - \theta \cos \theta) \]
...