Physical
Interpretation of the partial derivative
∂f(x,y)/ ∂y
Consider a surface S
given by z =
f(x,y).
The intersection of the plane, PL, given
by x
= constant with the surface, S,
defines the curve of intersection,
C. Let the
tangent line to C
at point P with coordinates
(a, b, c) be
T.
|
Then the slope of the line tangent to the
curve C at the point (a,b,c) in the y-direction
is:
fy(x,y) = ∂f(x,y)/
∂y evaluated at the point
P (a,b,c)
Similarly one can
imagine a plane, y = constant, intersecting the surface z
along a curve D (not
shown).
The slope
of the line tangent to the curve D at the point (a,b,c)
in the x-direction is:
fx(x,y) = ∂f(x,y)/
∂x evaluated at the
point P (a,b,c)
|
|
Click here for an example. Click here for discussion of linear
approximation.
|