Consider the functions $z=-7e^{x}lny,x=ln(ucosv),$ and $y=$usinv.

$($a$)$ Express $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{u}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{v}}$ as functions of $u$ and $v$ both by using the Chain Rule and by expressing $z$ directly in terms of $u$ and $v$ before differentiating.

$($b$)$ Evaluate $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{u}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{v}}$ at $(u,v)=(7,\frac{}{4}).$