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If f(x, y) = xy, then the differential df is equal to

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BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)
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  1. xdx + ydy
  2. ydx + xdy
  3. dx + dy
  4. dx - dy

Answer (Detailed Solution Below)

Option 2 : ydx + xdy

Detailed Solution

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Concept:

If z = f(x,y)

then the change in z (total differential) is

 \(dz = \;\frac{{\partial z}}{{\partial x}}dx + \frac{{\partial z}}{{\partial y}}dy\)

Calculation:

Given:

z = xy
Then the total differential is

\(dz = \;\frac{{\partial (xy)}}{{\partial x}}dx + \frac{{\partial (xy)}}{{\partial y}}dy\)

z = ydx + xdy

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