Define f on R$^(2)$ by f$(0,0)=0,$ and

f$($s$,$t$)=($st$($s$^(2)-$t$^(2)))/($s$^(2)+$t$^(2))$

for $($s$,$t$)!=(0,0).$ Show that f is of class C$^(1)$ in R$^(2),$ and that the mixed

partial derivatives D$\_(1)$D$\_(2)$f and D$\_(2)$D$\_(1)$f exist at every point of R$^(2),$ but that

D$\_(1)$D$\_(2)$f$(0,0)!=$D$\_(2)$D$\_(1)$f$(0,0).$ PLEASE PROVIDE A COMPELTE AND RIGOROUS ARGUMENT. INCORRECT SOLUTIONS WILL BE DOWNVOTED