If x=a (cos t + t sin t) and y=a ( sin t- t cos t), find `(d^(2)y)/(dx^(2))`

Explanation

To find \(\frac{d^2y}{dx^2}\) given the parametric equations \(x = a(\cos t + t \sin t)\) and \(y = a(\sin t - t \cos t)\), we will follow these steps:

### Step 1: Find \(\frac{dx}{dt}\)
Differentiate \(x\) with respect to \(t\):
\[ \frac{dx}{dt} = \frac{d}{dt}[a(\cos t + t \sin t)] \]
Using the product rule on \(t \sin t\):
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