Suppose $f(x,y)=x^2+y^2+z^2,$ where $x=rcos(),y=rsin()$ and $z=r^2.$

$(a)(5$ points$)$ Which $of$ the following $is$ the correct formula for $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}}?$

$(A.)\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}}=\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{z}}\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}}$

$B.\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}}=\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}\frac{dx}{d}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}\frac{dy}{d}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{z}}\frac{dz}{d}$

$C\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}}=\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{z}}\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}$

$D.\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}}=\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{z}}\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{r}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}\text{r}}+\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{z}}\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{r}}$

$(b)(8$ points$)$ Determine $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}}at$ the point $(r,)=(3,)$