Taylor series expansion of $f(x_0+h, z_0+k_1)$

Question

I'm trying to understand the taylor series expansion of $f(x_0+h, z_0+k_1)$

It is given by:

$f(x_0+h, z_0+k_1)= f(x_0, z_0)+ h*\frac{\partial f(x_0, z_0)}{\partial x}+ k_1*\frac{\partial f(x_0, z_0)}{\partial y}+...$

But what is the general rule? I can't find it.