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Homework Help: Having some trouble differentiating

  1. Oct 6, 2005 #1
    I'm having some trouble differentiating [itex] x^{\sqrt x } [/itex]. I know that the derivative of [itex] x^{\sqrt x } [/itex] probably begins with [itex] x^{\sqrt x } \cdot \ln (x) \cdot \frac{1}{{2\sqrt x }} [/itex] but once the base is also x then there is probably more to it than that. Anyone?
  2. jcsd
  3. Oct 6, 2005 #2


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    You have [tex] y=x^{\sqrt x } [/tex]
    So, [tex] \ln y = (\sqrt x)(\ln x) [/tex]
    Then differentiate both sides with respect to x and substitute the value of y.
  4. Oct 6, 2005 #3
    Ah, yes, thanks siddharth!
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