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Differentiate the following w.r.t x: If y = sin-1\(\left(\cfrac{2\text x}{1+\text x^2}\right)\) + sec-1\(\left(\cfrac{1+\text x^2}{1-\text x^2}\right)\)

show that dy/dx = 4/(1 + x2).

sin-1(2x/1 + x2) + sec-1(1 + x2)/(1 - x2),

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Given: Value of y = sin-1\(\left(\cfrac{2\text x}{1+\text x^2}\right)\) + sec-1\(\left(\cfrac{1+\text x^2}{1-\text x^2}\right)\)

To prove: \(\cfrac{dy}{d\text x}=\cfrac{4}{(1+\text x^2)}\) 

The formula used: (i) cos θ  = sin\(\left(\cfrac\pi2-\theta\right)\)

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