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Question: If y = sin<sup>–1</sup> [\(\sqrt{x - ax}\)–\(\sqrt{a - ax}\)], then \(\frac{dy}{dx}\)is equal to-...

If y = sin–1 [x−ax\sqrt{x - ax}–a−ax\sqrt{a - ax}], then dydx\frac{dy}{dx}is equal to-

A

1sin⁡a−ax\frac{1}{\sin\sqrt{a - ax}}

B

sin x\sqrt{x}. sin a\sqrt{a}

C

12x1−x\frac{1}{2\sqrt{x}\sqrt{1 - x}}

D

Zero

Answer

12x1−x\frac{1}{2\sqrt{x}\sqrt{1 - x}}

Explanation

Solution

Put x = sin2 q & a = sin2 f

then y = sin–1 (sin q cos f – cos q sin f)

= sin–1 (sin (q –f))

y = q – f = sin–1 x\sqrt{x} – sin–1 a\sqrt{a}

dydx\frac{dy}{dx}= 11−x\frac{1}{\sqrt{1 - x}}× 12x\frac{1}{2\sqrt{x}}