A) \[\frac{dy}{dx}=\frac{y}{\sqrt{1-{{x}^{2}}}}\]
B) \[\frac{dy}{dx}=\frac{1}{\sqrt{1-{{x}^{2}}}}\]\[\]
C) \[\frac{dy}{dx}=\frac{x}{\sqrt{1-{{x}^{2}}}}\]
D) None of these
Correct Answer: A
Solution :
\[y=c{{e}^{{{\sin }^{-1}}x}}\]. Differentiate it w.r.t. x, we get \[\frac{dy}{dx}=c{{e}^{{{\sin }^{-1}}x}}.\frac{1}{\sqrt{1-{{x}^{2}}}}=\frac{y}{\sqrt{1-{{x}^{2}}}}\] or \[\frac{dy}{dx}=\frac{y}{\sqrt{1-{{x}^{2}}}}\].
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