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Tricky Differentiation of Derivative

  1. Nov 18, 2008 #1
    I am having trouble remembering the correct approach here. This is in regards to deriving a governing equation for conservation of momentum for a non-newtonian fluid. I thought about posting in engineering, but it is more of a calculus question:

    d/dx(((-dv/dx)^(m-1))*(dv/dx)) where we are differentiating with respect to x, v is a function of x, and m is some value, not necessarily in integer.

    I thought about treating dv/dx as f(x) and doing the chain rule and then the product rule, but am unsure. This step is skipped in the derivation I am looking at, and I would love to figure out the math behind it. Thanks!
  2. jcsd
  3. Nov 19, 2008 #2


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    Hi olechka722! :smile:

    If you mean d/dx{(dv/dx)m-1(dv/dx)},

    that's just d/dx{(dv/dx)m},

    = m(dv/dx)m-1d2v/dx2
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