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Math Help - Partial Derivatives

  1. #1
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    Partial Derivatives

    Hi all,

    my homework questions states "f(x,y)=sin(x-y) at the point (-3,-3)".

    • I distributed sin, and obtained sinx-siny
    • holding y constant and differentiating with respect to x, i obtain fx(x,y)=cosx
    • the derivative of cos(x) is xcos(x), or -3cos(-3)
    • holding x constant and differentiating with respect to y, i obtain fy(x,y)=-cosx
    • the derivative of -cos(x) is 3 cos(-3)

    for some reason, my answers are wrong. I was wondering if someone could help me walk through the steps. Thank you in advance.
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  2. #2
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    Quote Originally Posted by newman611 View Post
    Hi all,

    my homework questions states "f(x,y)=sin(x-y) at the point (-3,-3)".

    • I distributed sin, and obtained sinx-siny
    • holding y constant and differentiating with respect to x, i obtain fx(x,y)=cosx
    • the derivative of cos(x) is xcos(x), or -3cos(-3)
    • holding x constant and differentiating with respect to y, i obtain fy(x,y)=-cosx
    • the derivative of -cos(x) is 3 cos(-3)

    for some reason, my answers are wrong. I was wondering if someone could help me walk through the steps. Thank you in advance.
    sorry, but \sin(x-y) \ne \sin{x} - \sin{y}

    review your trig identities ...

    \sin(x-y) = \sin{x}\cos{y} - \cos{x}\sin{y}
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  3. #3
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    Oh, I see my mistake! Thank you!
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