Problem $2.$ Let $f(x,y)be$ a function $of$ two variables $s$ and $t$ defined $by$ the equations

$x=s+t$ and $y=s-t.$ Verify that

$(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}{)}^2-(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}{)}^2=(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{s}})(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{t}})$