xplain why the function is differentiable at the given point.

f$($x$,$ y$)=2+$ x ln$($xy $7),(2,4)$

The partial derivatives are

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

and

fy$($x$,$ y$)=$

$,$

so

fx$(2,4)=$

and

fy$(2,4)=.$

Both

fx

and

fy

are continuous functions for

$,$

so f is differentiable at

$(2,4).$

Find the linearization

L$($x$,$ y$)$

of

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

at

$(2,4).$

L$($x$,$ y$)=$