# F(x)=x^log(x) differentiation

1. Jan 16, 2009

### Fairy111

1. The problem statement, all variables and given/known data
Find the derivative of the following function f.

2. Relevant equations

f(x)=x^log(x)

3. The attempt at a solution

I really don't know how to do this, as it's x to the power of a function of x.

2. Jan 16, 2009

### D H

Staff Emeritus
Re: differentiation

Use the fact that for any function u(x),

$$u(x) = e^{\ln(u(x))}$$

3. Jan 16, 2009

### HallsofIvy

Staff Emeritus
Re: differentiation

Or (almost the same thing) use "logarithmic differentiation".

If y= xlog x then log(y)= log(xlog(x))= log(x)log(x).

Differentiate both sides with respect to x, using the chain rule on the left side, and then solve for dy/dx.