Homework Help: Having some trouble differentiating

1. Oct 6, 2005

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?

2. Oct 6, 2005

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.

3. Oct 6, 2005

TSN79

Ah, yes, thanks siddharth!