Partial Derivatives of Functions (continued)
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,
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)
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