Find the following derivatives.

$($a$)$ Find $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}$ for $f(x,y)=\frac{x}{x^2{y}^2}.$

$($b$)$ Find uxx, $u_{xy}$ and $u_{yy}$ for $\backslash$times $).$

$($c$)$ Find $\frac{\text{d}\text{e}\text{l}\text{Q}}{\text{d}\text{e}\text{l}\text{L}},\frac{\text{d}\text{e}\text{l}\text{Q}}{\text{d}\text{e}\text{l}\text{M}},$ and $\frac{\text{d}\text{e}\text{l}\text{Q}}{\text{d}\text{e}\text{l}\text{t}}$ for $Q=LM{e}^{Mt}.$