- #1
chexmix
- 8
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Homework Statement
I am working on a homework problem involving partial derivatives. I've been checking my answers against what Wolfram Alpha spits out just for extra assurance. For the following problem
Find all the second partial derivatives: v = [itex]\frac{xy}{(x-y)}[/itex].
When I get to the point where I am deriving v[itex]_{xy}[/itex], Wolfram Alpha gives me
[itex]\frac{2xy}{(x-y)^3}[/itex]
but I get something different. If someone can tell me where I am going wrong here, I would be most grateful: I've stared at this for some time now. I suspect it is something very trivial. I am using the quotient rule.
2. The attempt at a solution
[itex]\frac{\partial}{\partial y}[/itex] [itex]\frac{y^2}{(x-y)^2}[/itex]
[itex]\frac{(x-y)^2 * 2y - y^2 * (2 (x-y))}{(x-y)^4}[/itex]
[itex]\frac{(x-y)((x-y)*2y - 2y^2)}{(x-y)^4}[/itex]
[itex]\frac{2xy-4y^2}{(x-y)^3}[/itex]
Thanks,
Glenn