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Math Help - derivative question.

  1. #1
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    derivative question.

    Ok so I'm having a little trouble figuring out which method I am supposed to use to solve this problem.

    Calculate the derivative of f(x,y)= (y-x^2)/3y along the curve parameterized by r(t)= 2t(i) - t^(1/2)(j) when t=4.

    Do I put the 4 in for t and then use that as the direction and find the directional derivative, or is this a chain rule problem where I take
    df/dx * dx/dt + df/dy * dy/dt? Any help would be greatly appreciated. Thanks.
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  2. #2
    Super Member Aryth's Avatar
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    It would be the second option. It is not asking you to find the rate of change in the direction of \bold{r}, it is asking for the rate of change of the function along the parametrized curve. You would need to use the differential method.
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  3. #3
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    Ok. so I made it through using this method, and I'm thinking that I should be able to set x=2t and y= -t^(1/2) insert the t=4 and solve, then insert these into my final differential giving me a scalar answer since the original function is parameterized by r(t)= 2t(i) - t^(1/2)(j). Is this correct?
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