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Question: If y = sec<sup>–1</sup>\(\frac{\sqrt{x} - 1}{x + \sqrt{x}}\)+ sin<sup>–1</sup>\(\frac{x + \sqrt{x}}{...

If y = sec–1x−1x+x\frac{\sqrt{x} - 1}{x + \sqrt{x}}+ sin–1x+xx−1\frac{x + \sqrt{x}}{\sqrt{x} - 1} then dydx\frac{dy}{dx} is equal to –

A

x

B

1

C

0

D

None of these

Answer

0

Explanation

Solution

f(x) = cos–1x+xx−1\frac{x + \sqrt{x}}{\sqrt{x} - 1}+ sin–1(x+xx−1)\left( \frac{x + \sqrt{x}}{\sqrt{x} - 1} \right)

f(x) = π2\frac{\pi}{2} ⇒ f ′(x) = 0