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Question
If v(x, y) = `x^2 - xy + 1/4 y^2 + 7, x, y ∈ "R"`, find the differential dv
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Solution
First let us find vx, vy
Now, vx = `(del"v")/(delx)` = 2x – y
vy = `(del"v")/(dely) = - x + 1/2 y`
The differential is
dv = vx dx + vy dy
dc = `(2x - y) "d"x + (1/2 y - x) "d"y`
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