Upload
zoe-mckenzie
View
218
Download
1
Embed Size (px)
Citation preview
13.3 Partial derivativesFor an animation of this concept visit
http://www.math.umn.edu/~rogness/multivar/dirderiv.shtml
yx
z
2 2, 100f x y x y
10
10
100
When we have functions with more than one variable, we can find partial derivatives by holding all the variables but one constant.
2df
xdx
2
22
d f
dx
2df
ydy
2
22
d f
dy
Note:df
dxis also written as xf (eff sub ecks)
Notation for First Partial Derivatives
yx
z
2 2, 100f x y x y
10
10
100
2df
xdx
2df
ydy
df
dxwould give you the slope of the tangent in the plane y=0 or in any plane with constant y.
In other words, how is changing one variable going to change the value of the function?
Definition of Partial Derivatives of a Function of Two Variables
f(x,y) = e x y , find fx and fy And evaluate each at the point (1,ln2)
2
Example 2
Diagram for example 2
Example 2 solution
Example 3
Find the slope in the x-direction and in the
y-direction of the surface given by
When x=1 and y=2
Solution to example 3
Example 4
Find the slope of the given surface in the
x-direction and the y-direction at the point (1,2,1)