Differentiating

[TSN79]

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?

[siddharth]

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.

[TSN79]

Ah, yes, thanks siddharth!