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Question: If y = tan<sup>–1</sup>\(\left( \frac{x}{\sqrt{1 + x^{2}} - 1} \right)\)then \(\frac{dy}{dx}\)is-...

If y = tan–1(x1+x2−1)\left( \frac{x}{\sqrt{1 + x^{2}} - 1} \right)then dydx\frac{dy}{dx}is-

A

12(1+x2)\frac{1}{2(1 + x^{2})}

B

−12(1+x2)\frac{- 1}{2(1 + x^{2})}

C

1+x22\frac{1 + x^{2}}{2}

D

−(1+x2)2\frac{- (1 + x^{2})}{2}

Answer

−12(1+x2)\frac{- 1}{2(1 + x^{2})}

Explanation

Solution

Put x = tan q to get y = π2\frac{\pi}{2}–12\frac{1}{2}tan–1 x