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Math Help - partial derivative, help please

  1. #1
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    Smile partial derivative, help please

    Hi,
    This is my first post so I do not know how to properly insert the partial derivative symbol, therefore d stands not for derivative but for partial derivative.


    I have been trying to solve this exercise since Friday and I have no idea what to do:
    Compute
    d^(137)f / [(dx^(72))(dy^3)(dx)(dx)(dy^(60))]
    for f(x,y) = cos (2x y)
    Any suggestions will help

    thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alekb View Post
    Hi,
    This is my first post so I do not know how to properly insert the partial derivative symbol, therefore “d” stands not for derivative but for partial derivative.


    I have been trying to solve this exercise since Friday and I have no idea what to do:
    Compute
    d^(137)f / [(dx^(72))(dy^3)(dx)(dx)(dy^(60))]
    for f(x,y) = cos (2x – y)
    Any suggestions will help

    thanks!
    ouch! i'm assuming you mean \frac {\partial ^{137} f}{\partial x^{72} \partial y^3 \partial x \partial x \partial y^{60}}

    Basically what this is asking you to do is differentiate f with respect to y 60 times, then the resulting function with respect to x twice, then that resulting function with respect to y three times, then finally the resulting function with respect to x 72 times.

    in each case, i'd just do it a few times and try to pick up a pattern of what it would look like after doing it 60 and 72 times. good luck. seems like it will be a pain, but maybe not as hard as you think. maybe.
    Last edited by Jhevon; January 10th 2010 at 07:13 PM. Reason: added a little bit of clarification
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  3. #3
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    Indeed, that's what I meant.

    So, can I combine those partial derivatives and then multiply both results?(differentiate f with respect to y 63 times and f with respect to x 74 times), or do I need to follow the order that you posted?

    Thanks!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alekb View Post
    Indeed, that's what I meant.

    So, can I combine those partial derivatives and then multiply both results?(differentiate f with respect to y 63 times and f with respect to x 74 times), or do I need to follow the order that you posted?

    Thanks!
    no multiplication goes on here. you just differentiate the function over and over (that is, differentiate the function, then differentiate the result, then differentiate that result, etc). and yes, it has to be in the exact order i said.
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