Let $f(x,y,z)=x^5{y}^4+z^4$ and $x=s^5,y=s{t}^5,$ and $z=s^{5}t.$

$(a)$ Calculate the primary derivatives $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}},\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}},\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{z}}.$

$(Use$ symbolic notation and fractions where needed.$)$

$\frac{i}{i}$

$\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=$