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Total differential Problem

  1. May 29, 2016 #1
    1. The problem statement, all variables and given/known data
    You have two parameters x = 12 and y = 3 set on a machine. The machine generates a function: z (x, y) = 3sin (x ^ 2 + y) y + x ^ 3
    Use the total differential of this function in the set point to determine which of the parameters to be set to the most accurate.
    2. Relevant equations
    dz = (∂z/∂x) dx + (∂z/∂y) dy
    3.Solution
    z = 3y sin(x²+y) + x^3

    dz = (3y cos(x²+y) * 2x + 3x²) dx + (3 sin(x²+y) + 3y cos(x²+y) * 1 + 0) dy
    dz = (6xy cos(x²+y) + 3x²) dx + (3 sin(x²+y) + 3y cos(x²+y)) dy

    I don't understand why (∂z/∂y) = (3 sin(x²+y) + 3y cos(x²+y) * 1 + 0) dy Where did that zero came from ??? and 1 ??
     
  2. jcsd
  3. May 29, 2016 #2

    BvU

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    So, NN, where is your attempt at solution ?
    What would be your ##\partial z\over \partial y## ?
     
  4. May 29, 2016 #3
    Writing he zero is kind of unnecessary, but it comes from taking the partial derivative of x3 with respect to y. The 1 comes from the y...chain rule.
     
  5. May 29, 2016 #4

    BvU

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    Did you notice the posting in 'homework' ? It is not good for the poster and it is against PF rules to give such a direct answer: it robs the poster from an opportunity to learn from insight.
     
  6. May 29, 2016 #5
    (3 sin(x²+y) + 3y cos(x²+y) * 1 + 0) dy
     
  7. May 29, 2016 #6
    Oh I see, thank you very much
     
  8. May 29, 2016 #7
    You're welcome.
     
  9. May 29, 2016 #8
    Nope, I didn't notice. I'll likely avoid answering posts in this section from now on.
     
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