Posted by mark on Sunday, October 5, 2008 at 3:52pm.
dZ = Zx dx + Zy dy (1)
dZ = df = fu du + fv dv (2)
Express du and dv in terms of dx and dy:
du = ux dx + uy dy (3)
dv = vx dx + vy dy (4)
Substitute (3) and (4) in (2):
dZ = fu (ux dx + uy dy ) + fv (vx dx + vy dy) =
(fu ux + fv vx) dx + (fu uy + fv vy)dy
Comparing this to (1) then gives:
Zx = fu ux + fv vx
Zy = fu uy + fv vy
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