Problem

二、多選題（占 32 分）

11. 當 $f(x,y)=x^2+y^2+\exp(x-y)$，且 $F(x,y,z)=f(x,y)-z$。請問下列哪些選項是正確的？

(A) $\dfrac{\partial f}{\partial x}+\dfrac{\partial f}{\partial y}=2x+2y$

(B) $\dfrac{\partial^2 f}{\partial x^2}-\dfrac{\partial^2 f}{\partial y^2}=2\exp(x-y)$

(C) $\nabla F$ at the point $(1,2,-1)$ is $(1,3,-1)^T$

(D) The tangent plane to the graph of the function $F(x,y)$ at the point $(1,1,3)$ is $3(x-1)+(y-1)-(z-3)=0$.

(E) The minimum value of $f(x,y)$ is $0$。