A) \[0\]
B) \[-1\]
C) \[-2\]
D) \[1\]
E) \[2\]
Correct Answer: E
Solution :
\[y={{({{\sin }^{-1}}x)}^{2}}\] Differentiating on both sides, \[\frac{dy}{dx}=2{{\sin }^{-1}}x.\frac{1}{\sqrt{1-{{x}^{2}}}}\] \[\Rightarrow \] \[\sqrt{1-{{x}^{2}}}=\frac{dy}{dx}=2{{\sin }^{-1}}x\] Differentiating on both sides, \[\sqrt{(1-{{x}^{2}})}\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{2}{2\sqrt{1-{{x}^{2}}}}\frac{dy}{dx}=\frac{2}{\sqrt{1-{{x}^{2}}}}\] \[2(1-{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}-2\frac{dy}{dx}.x=4\] \[\Rightarrow \] \[(1-{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}=2\]
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