Differentiating

TSN79

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?

siddharth

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.

TSN79

Ah, yes, thanks siddharth!