If $xy+\frac{x}{y}-3x+4y^2-2yz+7x{z}^3-xyz=0,$ find $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}$&$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}$ considering $z$ as a differentiable function of $x$&$y.$

If $f(x,y,z)=e^{x}yz$ and $\frac{?}{\text{b}\text{a}\text{r}}(r(t))=cos\frac{t}{b}ar()+3sin\frac{t}{b}ar(J)+\frac{t^3}{b}ar(k),$ find the rate of change of $f(x,y,z)$ along $\frac{?}{\text{b}\text{a}\text{r}}(r(t))$