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If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e ...

If `f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)=` 1 (b) `-1` (c) `0` (d) none of these

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Correct option is B)
` Let y=f(x) then y=frac{sin ^{-1} x}{sqrt{1-x^{2}}}`
` Rightarrow {y} sqrt{1-{x}^{2}}=sin ^{-1} {x}`
On differentiating w.r.t x we get
`Rightarrow y cdot frac{1}{2 sqrt{1-x^{2}}}(-2 x)+sqrt{1-x^{2}} frac{d y}{d x}=frac{1}{sqrt{1-x^{2}}} `
` ...
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