二元分段函数求导和连续的问题如图,关于这个分段函数想找一个使得关于x和关于y求导都存在的一个常数应该怎么做?还有如何证明

(a) c=1
fx(0,0)=lim(x→0)[f(x,0)-f(0,0)]/(x-0)=lim(x→0)[︱x︱-︱x︱]/[︱x︱(x-0)]
=lim(x→0)0/[︱x︱(x-0)]=0
fy(0,0)=lim(y→0)[f(0,y)-f(0,0)]/(y-0)=lim(y→0)[︱y︱-︱y︱]/[︱y︱(y-0)]
=lim(y→0)0/[︱y︱(y-0)]=0
(b)c=1 do not make f continuous at (0,0)
lim(y=kx,x→0)f(x,y)=[︱1-︱k︱︱]/(1+︱k︱)
This means lim((x,y)→(0,))f(x,y) does not exist .So we can not choose c differently that will make f continuous at (0,0)