For the functions $w=xy+yzxz,x=3u+v,y=3u-v,$ and $z=uv,$ express $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{u}}$ and $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{v}}u$ ing the chain rule and by expressing $w$ directly in terms of $u$ and $v$ before differentiating. Then evaluate $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{u}}$ and $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{v}}$ at the point

$(u,v)=(\frac{2}{3},-2)$

Express $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{u}}$ and $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{v}}$ as functions of $u$ and $v.$ Find $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{u}}.$

$\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{u}}=$