User:EGM6321.f12.team7.Marjanovic/report4/4.5

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Problem 6: Showing equivalence to symmetry of mixed 2nd partial derivatives of first integral
Based on lecture notes

section 22

Solution
We know that:

Putting this in the form given in ($$),

Now we collect the like terms:

From here we get:

Now if we expand out both sides of ($$), we get:

Setting them equal to each other, we get:

Similarly, from ($$) and ($$), we see that: