第1832题：对数求导法
求 y=(x1−x)xy=\Big ( \dfrac{x}{1-x} \Big )^xy=(1−xx)x 的导数 y′y'y′ .
A. (x1−x)x(lnx1−x+x1−x) \Big ( \dfrac{x}{1-x} \Big )^x \Big (\ln \dfrac{x}{1-x} +\dfrac{x}{1-x} \Big )(1−xx)x(ln1−xx+1−xx)
B. (x1−x)x(ln1−2x1−x+x1−x) \Big ( \dfrac{x}{1-x} \Big )^x \Big (\ln \dfrac{1-2x}{1-x} +\dfrac{x}{1-x} \Big )(1−xx)x(ln1−x1−2x+1−xx)
C. (x1−x)x\Big ( \dfrac{x}{1-x} \Big )^x(1−xx)x (lnx1−x+11−x)\Big ( \ln \dfrac{x}{1-x} +\dfrac{1}{1-x} \Big )(ln1−xx+1−x1)
D. (x1−x)x(lnx1−x+2x1−x)\Big ( \dfrac{x}{1-x} \Big )^x \Big (\ln \dfrac{x}{1-x} +\dfrac{2x}{1-x} \Big )(1−xx)x(ln1−xx+1−x2x)
