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

Explanation

To find \(\frac{dy}{dx}\) when \(x = \frac{2t}{1+t^2}\) and \(y = \frac{1-t^2}{1+t^2}\), we will use the chain rule and implicit differentiation. Here are the steps to solve the problem:

### Step 1: Differentiate \(x\) with respect to \(t\)
Given:
\[ x = \frac{2t}{1+t^2} \]
We will use the quotient rule to differentiate \(x\):
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