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Tutorial Exercise

Find the gradient vector field of f$.$

f$($x$,$ y$)=$ xe$8$xy

Step $1$

Recall that the gradient vector field of

f$($x$,$ y$)$

is the vector field

$$f$($x$,$ y$)=$ fx$($x$,$ y$)$i $+$ fy$($x$,$ y$)$j$.$

For

f$($x$,$ y$)=$ xe$8$xy$,$

fx must be found using the Product Rule. We get the following.

fx$($x$,$ y$)=$

x

$+$

e$8$xy

$=$

e$8$xy