Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 12 / a / i

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- Solution i

Solution

The two coefficients are the corresponding partial derivatives of

e^{x + y}

. Therefore the differential form is exact, with

f (x, y) = e^{x + y} + C, df = e^{x + y} d x + e^{x + y} d y .

The arbitrary constant does not change the total differential.

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