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Differentiate tan^(-1)((sqrt(1+x^2)-1)/x...

Differentiate `tan^(-1)((sqrt(1+x^2)-1)/x)` with respect to `tan^(-1)x ,x!=0.`

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To differentiate \( u = \tan^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right) \) with respect to \( v = \tan^{-1}(x) \), we will follow these steps: ### Step 1: Define the Variables Let: - \( u = \tan^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right) \) - \( v = \tan^{-1}(x) \) ### Step 2: Find \(\frac{du}{dx}\) ...
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