Exponential/Logarithmic functions

[nvrslep303]

Homework Statement

Find the derivative of
y = sqrt(X^X)

The Attempt at a Solution

I tried using the equation d/dx (a^x) = a^x * ln a

Is this even a right start? The square root kind of throws me off. I'm not sure if this is the right equation to use or not. I was told the answer was

X^x / (2*sqrt(X^x)) but I'm not even sure how to get there given the answer. any hints or help? :(

 

[Dick]

x=e^log(x). So x^x=e^(log(x)*x). Try treating it that way. Your given equation is only valid for 'a' being a constant. You can handle the sqrt by either using the chain rule or just the rules of exponents. sqrt(x^x)=(x^x)^(1/2)=x^(x/2), right?

 

[lanedance]

how about starting by writing as
$$y = \sqrt{x^x} = (x^x)^{\frac{1}{2}}$$

then simplify and consider taking the log of both sides and implicit differentiation