For the functions $w=xy+yz+xz,x=u+2v,y=u-2v,$ and $z=uv,$ express $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{u}}$ and $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{v}}$ using 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 $(u,v)=(\frac{3}{4},4).$