The function f(x,y) is a function of the two variables x and y.
If f(x,y) is continuous and it has derivatives in all directions,
then we may define * partial derivatives * in the following manner:

We will write ``f_{x}(x,y)'' to represent **the partial derivative
of f(x,y) with respect to x**. Symbolically, this is computed by
computing the derivative of f with respect to x, treating the occurrences
of the variable y as constants. For example, if

f(x,y) = x^{3} + y^{3} + 6xy

then f_{x}(x,y) = 3x^{2} + 6y.

Likewise, f_{y}(x,y) is **the partial derivative with respect to y,**
symbolically computed by taking the derivative with respect to y,
treating x as a constant:

f(x,y) = x^{3} + y^{3} + 6xy, then

f_{y}(x,y) = 3y^{2} + 6x.