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Math Help - Chain Rule & Substitution in Partial Derivatives

  1. #1
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    Chain Rule & Substitution in Partial Derivatives

    THIS IS MY EFFORT:
    I just wanted to know if there are mistakes in my work...

    #1


    #2



    THANKS FOR THOSE WHO WILL HELP ^_^
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  2. #2
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    Those are correct. However, I notice that in using chain rule for the second problem, you have
    \frac{\partial u}{\partial t}= 2e^{\frac{y}{x}}sec^2 t
    while using direct substitution, you get
    \frac{\partial u}{\partial t}= 2e^{2tan t}sec^2 t

    Those are, of course, the same because x= 2r cos t and y= 4r cos t so that \frac{y}{x}= \frac{4r cos t}{2r cos t}= 2 tan t

    but the second, with only the variable t is the better expression.
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  3. #3
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    oh yeah!! since it is with respect to t..thanks a lot for that one...

    however, i am just wondering in my number 1 answer...try to take a look in Chain Rule the y=re^-s, are the derivatives under it are correct??
    Last edited by cutiemike1; October 7th 2010 at 04:51 AM.
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  4. #4
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    oh yeah!! since it is with respect to t..thanks a lot for that one...

    however, i am just wondering in my number 1 answer...try to take a look in Chain Rule ung y=re^-s, are the derivatives under it are correct??
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