Partial Derivatives
CJHL2012
Page 1
3.
PARTIAL DERIVATIVES
3.0
Function of Several Variables
A function of a single variable y = f(x) is interpreted graphically as a planar curve.
In this section we shall see that a function of two variables z = f(x,y) can be
interpreted as a surface. Function of two or more variables often arise in
engineering and in science and it is important to be able to deal with such
functions with confidence and skill.
Example 1
Given
f(x,y,u) = x
2
+ yu + 2,
find
f(0,1,0), f(-1,-1,2).
f(x,y,u) =
The graphs of functions of two variables,
z
=
f
(
x
,
y
)
are surfaces in three
dimensional space. For example here is the graph of
z
=
2
2
y
x
+