Find `(dy)/(dx),` when `x=(3a t)/(a+t^2)"and"y=(3a t^2)/(1+t^2)`

Explanation

To find \(\frac{dy}{dx}\) given the equations \(x = \frac{3at}{a + t^2}\) and \(y = \frac{3at^2}{1 + t^2}\), we will use the chain rule and find \(\frac{dy}{dt}\) and \(\frac{dx}{dt}\) first.

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

Given:
\[ y = \frac{3at^2}{1 + t^2} \]
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