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Differentiate the following w.r.t x: tan-1\(\left(\cfrac{a\text x-b}{b\text x+a}\right),\) prove that dy/dx = \(\cfrac{1}{(1+\text x^2)}\)

 tan-1(ax - b)/(bx + a)

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Given: Value of  tan-1\(\left(\cfrac{a\text x-b}{b\text x+a}\right)\) 

tan-1(ax - b)/(bx + a)

To Prove: dy/dx = \(\cfrac{1}{(1+\text x^2)}\)

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

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