(B.)(partial f(x,y))/(partial x)连续，f(x,y)不可微. (C.)(partial f(x,y))/(partial x)不连续，f(x,y)可微. (D.)(partial f(x,y))/(partial x)不连续，f(x,y)不可微.

注类似地，已知函数$f(x,y)=\begin{cases}(x^{2}+y^{2})\cdot \sin \frac{1}{xy},&xy\neq 0,\\0,&xy=0,\end{cases}$则在点$(0,0)$处 (
A.)$\frac{\partial f(x,y)}{\partial x}$连续，$f(x,y)$可微. (
B.)$\frac{\partial f(x,y)}{\partial x}$连续，$f(x,y)$不可微. (
C.)$\frac{\partial f(x,y)}{\partial x}$不连续，$f(x,y)$可微. (
D.)$\frac{\partial f(x,y)}{\partial x}$不连续，$f(x,y)$不可微.

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