A) \[\frac{1}{\sqrt{1-x}}\]
B) \[\frac{-1}{2\sqrt{1-x}}\]
C) \[\frac{1}{\sqrt{x}}\]
D) \[\frac{-1}{2\sqrt{x}\sqrt{1-x}}\]
E) \[\frac{1}{\sqrt{x}\sqrt{1-x}}\]
Correct Answer: D
Solution :
Given that, \[y={{\sin }^{-1}}\sqrt{1-x}\] Differentiating w.r.t.\[x,\]we have \[\frac{dy}{dx}=\frac{1}{\sqrt{1-(1-x)}}.\frac{1}{2}.\frac{1}{\sqrt{1-x}}.(-1)\] \[=\frac{1}{\sqrt{x}}.\frac{(-1)}{2\sqrt{1-x}}\] \[=\frac{(-1)}{2\sqrt{x}.\sqrt{1-x}}\]
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