# Derivative of Square Root

1. Mar 22, 2009

### ssmh

I can't figure out
Derivative of (sq. rt of x)^x

Can anyone help me?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 22, 2009

### djeitnstine

Welcome to PF =]

Use the chain rule, this is simply a function within another function. the outer function just happens to be an exponential. $$\frac{d}{dx}f^x=f^x ln(f)$$ (if I remember correctly)

3. Mar 22, 2009

### tnutty

if this is what you mean :

find f(x) prime, where f(x) = sqrt(x)^x

Before I help you, you need to help me. Tell me what concept you have learned that could
apply to this problem

4. Mar 23, 2009

### HallsofIvy

Staff Emeritus
No, that's incorrect.

5. Mar 23, 2009

### MeTh0Dz

Here's how I did it.

$$\frac{d}{dx}$$(xx/2)

$$\frac{d}{dx}$$e(x/2)ln(x)

(1/2)(1 + ln(x))e(xln(x))/2

$$\frac{1 + ln(x)}{2}$$ * x(x/2)

6. Mar 23, 2009

### Jacobpm64

looks good to me.