Math 21a, Fall 2008
Exhibits page Math 21a 2008, Multivariable Calculus
The meaning of the mixed partial derivative fxy
Office: SciCtr 434
What does fxy mean?
Assume we have a function f(x,y) of two variables like f(x,y) = x2 y.
The partial derivative fx is the rate of change of the
function f in the x direction. We also can see that xx means:
it is positive if the surface is bent concave up in the x direction and negative
if it is bent concave down in the x direction.
What it the interpretation of the derivative fxy?
One can interpret it as the rate of change of the slope in the x-direction
as one moves into the y direction.
Can we read of the value of
from a level curves?
For one of the following contour maps, the derivative fxy
nonzero at the center of the picture. For which one?