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Derivative of log proof question

  1. Feb 29, 2012 #1

    d/dx [log[itex]_{b}x[/itex]] = d/dx (lnx/lnb) = 1/lnb d/dx(lnx) = 1/xlnb , when x>0

    I think I see the constant multiple rule at work here, but why? Is it because 1/lnb is a constant, so it is "factored" out of lnx/lnb and treated as a constant while lnx is treated as the term to be differentiated?
  2. jcsd
  3. Feb 29, 2012 #2


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    Exactly. ln(b) is just a constant factor, like 2.
  4. Mar 1, 2012 #3
    cool thanks
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