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

Question

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