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Partial derivative with chain rule: check work

  1. Mar 30, 2014 #1


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    1. The problem statement, all variables and given/known data

    If possible, please check my work for any large errors.

    y = 10kl - √k - √l
    k = (t/5) + 5
    l = 5e^t/10

    Evaluate at t = 0 using chain rule.

    2. Relevant equations

    y = 10kl - √k - √l
    k = (t/5) + 5
    l = 5e^t/10

    3. The attempt at a solution

    = ∂y/∂k * dk/dt + ∂y/∂l * dl/dt
    = (10l - 0.5K^-0.5)(1/5) + (10k - 0.5l^-.05)((e^(x/10))/2)

    k(0) = 5
    l(0) = 5
    y(0) = ~9.95 + ~41.03 = ~51
  2. jcsd
  3. Mar 31, 2014 #2


    Staff: Mentor

    The above is close. The -0.5l^(-.05) term should be -0.5l^(-0.5). I don't know if that was a transcription error. Also, the exponential term would be clearer as (1/2)e(x/10).
    k(0) and l(0) are fine, but I didn't check your other numbers.

    One other thing. It's not good to start your first line with "=". For your problem, you should start with dy/dt = ...
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