How Do You Differentiate e^(x^(x^2))?

[erjkism]

derivative of e^x^x^2??

can someone explain to me how this could be solved?

so far i have:
f(x)=e^x^x^2
lnf(x)= x^2lne^x)

(e and ln cancel?)

f'(x)/f(x)= (x^2)x
f'(x)= f(x) x^3

= (e^x^x^2)(x^3)??


is that right? or do i need to use the power rule or something?

 

[rock.freak667]

$$y=e^{x^{x^2}}$$
$$lny=x^{x^2}$$
use the fact that if $$Y=u^v$$
then $$\frac{1}{Y}\frac{dY}{dx}=\frac{v}{u}\frac{du}{dx}+\frac{dv}{dx}lnu$$