## Differentiating

I'm having some trouble differentiating $x^{\sqrt x }$. I know that the derivative of $x^{\sqrt x }$ probably begins with $x^{\sqrt x } \cdot \ln (x) \cdot \frac{1}{{2\sqrt x }}$ but once the base is also x then there is probably more to it than that. Anyone?

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 Recognitions: Gold Member Homework Help You have $$y=x^{\sqrt x }$$ So, $$\ln y = (\sqrt x)(\ln x)$$ Then differentiate both sides with respect to x and substitute the value of y.
 Ah, yes, thanks siddharth!