If $u=lx+my,v=mx-ly,$ show that $(\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}{)}_y*(\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{u}}{)}_v=\frac{l^2}{l^2+m^2},(\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}\text{v}}{)}_x(\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{y}}{)}_m=\frac{l^2+m^2}{l^2}.$