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Total differential

  1. May 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Calculate d (x * y ^ 4) if x = 2, y = 3, dx and dy = 0.02 = -0.03

    2. Relevant equations
    Total differential


    3. The attempt at a solution

    product rule:

    d(xy^4) = d/dx (xy^4) dx + d/dy (xy^4) dy
    d(xy^4) = y^4 dx + 4xy^3 dy

    When x = 2, y = 3, dx = 0.02, y = −0.03
    d(xy^4) = (3)^4 (0.02) + 4(2)(3)^3 (−0.03) = 1.62−6.48 = −4.86

    Why is d/dy(xy^4)dy not = 4y^3dy but its 4xy^3dy ???
     
    Last edited by a moderator: May 28, 2016
  2. jcsd
  3. May 28, 2016 #2
    What makes you think that it is 4y^3, what happened to x?
    Since the derivation is with respect to y the x will behave like a constant. So it's 4xy^3.
     
  4. May 28, 2016 #3
    Oh I thought you had to remove x . Now I understand thank you
     
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