A) \[\sqrt{x}\]
B) \[-\sqrt{x}\]
C) \[\frac{1}{\sqrt{x}}\]
D) \[-\frac{1}{\sqrt{x}}\]
Correct Answer: C
Solution :
Let \[y={{\cos }^{-1}}\sqrt{x}\]and \[z=\sqrt{1-x}\] \[\therefore \frac{dy}{dz}=\frac{\frac{-1}{\sqrt{1-x}}\times \frac{1}{2\sqrt{x}}}{-\frac{1}{2\sqrt{1-x}}}=\frac{1}{\sqrt{x}}\].
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