设 $z= \ln(x^2+y^2)$，则 $\displaystyle \frac{\partial^2{z}}{\partial{y^2}}=$（ ）.
A. $\displaystyle \frac{1}{(x^2+y^2)^2}$
B. $\displaystyle \frac{2(x^2-y^2)}{(x^2+y^2)^2}$
C. $\displaystyle \frac{2x^2}{(x^2+y^2)^2}$
D. $\displaystyle \frac{-2y^2}{(x^2+y^2)^2}$
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设 $z= \ln(x^2+y^2)$，则 $\displaystyle \frac{\partial{z}}{\partial{y}}$ 在点 $(1,2)$ 处的值为（ ）.
A. $\displaystyle\frac{4}{5}$
B. $\displaystyle\frac{2}{5}$
C. $\displaystyle\frac{1}{5}$
D. $-\displaystyle\frac{1}{5}$
设 $z=y \ln(xy)$，则 $\displaystyle \frac{\partial{z}}{\partial{y}}=$（ ）.
A. $\displaystyle\frac{y}{x}$
B. $\displaystyle\ln(xy)+\frac{1}{x}$
C. $\displaystyle\ln(xy)+\frac{1}{y}$
D. $\ln(xy)+1$
设 $z=y\ln(xy)$，则 $\displaystyle\frac{\partial {z}}{\partial {y}}=$（ ）.
A. $\displaystyle\frac{1}{y}$
B. $\displaystyle \ln(xy)+\frac{1}{x}$
C. $\displaystyle \ln(xy)+\frac{1}{y}$
D. $\displaystyle \ln(xy)+1$
设 $\displaystyle u=e^{-x}\sin\frac{x}{y}$，则 $\displaystyle \frac{\partial{u}}{\partial{y}}$ 在点 $\displaystyle (2,\frac{1}{\pi})$ 处的值为（ ）.
A. $\displaystyle -\frac{2\pi^2}{e^2}$
B. $\displaystyle \frac{2\pi^2}{e^2}$
C. $0$
D. $\displaystyle -\frac{1}{e^2}$
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