Consider the vector ficld $f(x,y,z)=\left[\begin{array}{c}6xz+2y^2{z}^2\\ 2x^{2}y+y{z}^3\\ x^2+3y^2+9z^2\end{array}\right]$

$($a$)$ Calculate the first partial derivative $\frac{?}{\text{b}\text{a}\text{r}}(del)\frac{\%}{b}ar(z)$

$($b$)$ Calculate the second partial derivative $de{l}^2$ydelxdely

$($c$)$ Calculate the second partial derivative $de{l}^2$ydelyox