Editing Graph of a function (section)

=== Functions of two variables ===

[[File:F(x,y)=−((cosx)^2 + (cosy)^2)^2.PNG|class=skin-invert-image|thumb|250px|Plot of the graph of <math>f(x, y) = - \left(\cos\left(x^2\right) + \cos\left(y^2\right)\right)^2,</math> also showing its gradient projected on the bottom plane.]]

The graph of the [[trigonometric function]]
<math display=block>f(x,y) = \sin(x^2)\cos(y^2)</math>
is
<math display=block>\{ (x, y, \sin(x^2) \cos(y^2)) : x \text{ and } y \text{ are real numbers} \}.</math>

If this set is plotted on a [[Cartesian coordinate system#Cartesian coordinates in three dimensions|three dimensional Cartesian coordinate system]], the result is a surface (see figure).

Oftentimes it is helpful to show with the graph, the gradient of the function and several level curves. The level curves can be mapped on the function surface or can be projected on the bottom plane.  The second figure shows such a drawing of the graph of the function:
<math display=block>f(x, y) = -(\cos(x^2) + \cos(y^2))^2.</math>