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Question: If y = sin<sup>–1</sup>\(\left( \frac{5x + 12\sqrt{1 - x^{2}}}{13} \right)\), then \(\frac{dy}{dx}\)...

If y = sin–1(5x+121−x213)\left( \frac{5x + 12\sqrt{1 - x^{2}}}{13} \right), then dydx\frac{dy}{dx}is equal to-

A

11−x2\frac{1}{\sqrt{1 - x^{2}}}

B

–11−x2\frac{1}{\sqrt{1 - x^{2}}}

C

31−x2\frac{3}{\sqrt{1 - x^{2}}}

D

None

Answer

11−x2\frac{1}{\sqrt{1 - x^{2}}}

Explanation

Solution

Put x = sin q

y = sin–1 {513.sin⁡θ+1213cos⁡θ}\left\{ \frac{5}{13}.\sin\theta + \frac{12}{13}\cos\theta \right\}

= sin–1 {cos q. cos a + sin q. sin a}

if 1213\frac{12}{13}= sin a then cos a = 513\frac{5}{13}

= sin–1 {sin (q + a)}

y = q + a = sin–1 x + a

dydx\frac{dy}{dx}= 11−x2\frac{1}{\sqrt{1 - x^{2}}}