# Derivative of Square Root

#### ssmh

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

Can anyone help me?
1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

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#### djeitnstine

Gold Member
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)

#### 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

#### HallsofIvy

Homework Helper
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)
No, that's incorrect.

#### 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)

#### Jacobpm64

looks good to me.

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