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STALIN [3.7K]
3 years ago
12

Compute the second partial derivatives

Mathematics
1 answer:
aliya0001 [1]3 years ago
8 0

f(x,y)=\log(x-y)

has first-order partial derivatives

\dfrac{\partial f}{\partial x}=\dfrac1{x-y}

\dfrac{\partial f}{\partial y}=-\dfrac1{x-y}

Then the second-order partial derivatives are

\dfrac{\partial^2f}{\partial x^2}=-\dfrac1{(x-y)^2}

\dfrac{\partial^2f}{\partial x\partial y}=\dfrac1{(x-y)^2}

\dfrac{\partial^2f}{\partial y\partial x}=\dfrac1{(x-y)^2}

\dfrac{\partial^2f}{\partial y^2}=-\dfrac1{(x-y)^2}

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