10
1. INTRODUCTION
Partial Derivatives
First-order partial derivatives: Consider a function f (x, y) defined on a region
R 2 R2. Let (a, b) be an interior point of R. The average rate of change as
you move horizontally from (a, b) to (a + h, b) is
f (a + h, b) f (a, b)
.
h
The instantaneous rate of change in the x-direction at (a, b) is
@f
f (a + h, b) f (a, b)
(a, b) = lim
,
h!0
@x
h
the partial derivative of f with respect to x.