Vector differentials. For these you must use partial differentiation. For each differential only operates on a specific variable. For example, $\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}$ would differentiate just on x leaving all constants AND other variables like, y $,$ and z unaffected in the differentiation. So$,$ if $f=x^2{y}^4,$ note this is a scalar function, and you were asked to find $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}$ it would equal $2x{y}^4.$ The differential operator is grad$=\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}$hat$()\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}$hat$()\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{z}}$hat$(k).$ Let's try one, note that the vector form is preserved in this operation. We will see this in calculating an electric field from an electric potential.

$21.$ Find gradf$=,$ if $f=25x^{-2}{y}^3{z}^{2}x7y$