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Questions  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Q)

Differentiate $x ^{\sin ^{-1} x}$ w.r.t $\sin^{-1} x$


$(A)\;x^{\sin^{-1}x}\begin{bmatrix} log\; x - \frac{\sqrt{1-x^2}}{x} \sin^{-1}x \end{bmatrix} $
$(B)\;x^{\sin^{-1}x}\begin{bmatrix} log\; x + \frac{\sqrt{1-x^2}}{x} \sin^{-1}x \end{bmatrix} $
$(C)\;x^{\sin^{-1}x}\begin{bmatrix}x\; log\; x + \frac{\sqrt{1-x^2}}{x} \sin^{-1}x \end{bmatrix} $
$(D)\;x^{\sin^{-1}x}\begin{bmatrix} x\;log\; x - \frac{\sqrt{1-x^2}}{x} \sin^{-1}x \end{bmatrix} $

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