Let f be a function of two variables x and y defined on an open region U -(x, y) and dx af (x, y) exist on U. If they are totally differen- ду such that both tiable at a point (a, b) e U, then show that - (а, b) дхду a²f (a,b). дудх This is due to Young (1909) and called the fundamental theorem of differen- tials. Note that no continuity for the partial derivatives are assumed. It is easily verified that xy(x² – y²) x² + y? if (x, y) # (0,0), f(x, y) = if (x, у) %3D (0,0), satisfies a²f -(0,0) = 1. дудх -(0,0) = -1 and дхду Check that this function does not satisfy the conditions stated in the problem.

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A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

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A: Explanation of the answer is as follows…

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A: Consider the given function

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A: In this question we have to find the correct answer.

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A: (a)

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A:

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A:

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A: