How Do You Differentiate (sqrt(x))^x?

[ssmh]

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

Can anyone help me?

 

[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)

 

[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]

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.

$$\frac{d}{dx}$$(x^x/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.