## Calculus (3rd Edition)

$$L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(y-b).$$
The linearization of $f(x,y)$ at $(a,b)$ is defined by $$L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(y-b).$$