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Given the function:$ f(x,y) = x^5y^4+\sin\left({x\over{y}}\right)$ How can I find such partial derivatives as $f_{xx}$, $f_{xy}$, $f_{yx}$, and $f_{yy}$?

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    I'm getting stuck in what exactly the notation is asking me to do. But if all it's asking is to basically take it twice then I think I got it.2012-11-26

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You have $f(x,y) = x^5y^4+\sin\left({x\over{y}}\right)$:

  • For $f_{xx}$ its asking you to take the derivative -- of the function -- twice of $x$ and treat $y$ as a constant. Same logic with $f_{yy}$

  • For $f_{xy}$ its asking you to take the derivative -- of the function -- of $x$ treat $y$ as a constant, then take the derivative of $y$ and treat $x$ as a constant. Same logic $f_{yx}$