For the following function

$f(x,y)=\sqrt[\phantom{2}]{(1-x^{\frac{2}{3}}{)}^3-y^2},$

$($a$)$ Find $f_x(\frac{1}{5},\frac{1}{7}),$

$($b$)$ Find $f_y(\frac{1}{5},\frac{1}{7}),$

$($c$)$ Find $f_{}(\frac{1}{5},\frac{1}{7}),$

$($d$)$ Find $f_{xy}(\frac{1}{5},\frac{1}{7}),$ and

$($e$)$ Find $f_{yy}(\frac{1}{5},\frac{1}{7})$