Find `(dy)/(dx)` , when `x=a\ (costheta+thetasintheta)` and `y=a(sintheta-thetacostheta)`

Explanation

To find \(\frac{dy}{dx}\) when \(x = a(\cos \theta + \theta \sin \theta)\) and \(y = a(\sin \theta - \theta \cos \theta)\), we will follow these steps:

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

Given:
\[ x = a(\cos \theta + \theta \sin \theta) \]
...