A) \[\frac{x}{y}\]
B) \[-\frac{x}{y}\]
C) \[\frac{y}{x}\]
D) \[-\frac{y}{x}\]
E) none of these
Correct Answer: B
Solution :
\[{{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{\pi }{2}\] \[\Rightarrow \] \[{{\sin }^{-1}}=\frac{\pi }{2}-{{\sin }^{-1}}y\] \[\Rightarrow \] \[{{\sin }^{-1}}={{\cos }^{-1}}y\] \[\Rightarrow \] \[y=\sqrt{1-{{x}^{2}}}\] On differentiating w.r.t.\[x,\]we get \[\frac{dy}{dx}=\frac{1}{2\sqrt{1-{{x}^{2}}}}(-2x)=-\frac{x}{y}\]
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