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Simple/annoying derivative

  1. Sep 4, 2006 #1
    Could som1 please explain how to derive y = x^(x^2-7):yuck:

    I started using the chain rule but got stuck wif the x base.


    thanx in advance
     
  2. jcsd
  3. Sep 4, 2006 #2

    HallsofIvy

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    Do you mean "find the derivative"? (Yes, "derive f(x)" can mean that but often it means "derive this formula".)

    Use "logarithmic differentiation". (In fact, I would expect a problem like this to be in a section of the book titled "logarithmic differentiation"!)

    If [itex]y= x^{x^2- 7}[/itex] then [itex]ln(y)= (x^2- 7)ln(x)[/itex].
    Can you differentiate both sides of that? Then solve for dy/dx.
     
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