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If y=(tan^(-1)x)^2 , then prove that (1+...

If `y=(tan^(-1)x)^2` , then prove that `(1+x^2)^2\ y_2+2x\ (1+x^2)y_1=2` .

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To prove that \((1+x^2)^2 y_2 + 2x(1+x^2)y_1 = 2\) for \(y = (\tan^{-1} x)^2\), we will follow these steps: ### Step 1: Differentiate \(y\) to find \(y_1\) Given: \[ y = (\tan^{-1} x)^2 \] Using the chain rule, we differentiate \(y\) with respect to \(x\): ...
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