Greg Kelly, Hanford High School, Richland, Washington.[r]
Trang 1y x
z
10
10
100
An Introduction to Partial Derivatives
Trang 2y x
z
, 100 2 2
f 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
2
df
x
2
d f
2
df
y
2
d f
Note: df
dx is also written as fx (eff sub ecks)
Trang 3y x
z
, 100 2 2
f x y x y
10
10
100
2
df
x
df
y
df
dx would 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?
Trang 4Mixed variables are also possible:
, cos x
f x y x y ye
df
y ye
dx
d df d
y ye
dy dx dy
2
d f
y e
dy dx
yx
f y e
df
x y e
dy
d df d
x y e
dx dy dx
2
d f
y e
dx dy
xy
f y e
, cos x
f x y x y ye
Both answers are the same!