Question

LGBADERIVATIVE:
Find the derivative
\[\huge f(x)=x^{x^{x}} \]

Answer 1

lol! DPAINCDERIVATIVE*

Answer 2

take the log a couple times

Answer 3

maybe ln it?
\[\ln y = x^x \ln x\]

side solution:
\[\ln a = x \ln x\]
\[\frac 1a a' = \ln x + 1\]
\[a' = (x\ln x)(\ln x+ 1)\]

so back to a while ago
\[\ln y = x^x \ln x\]
\[\frac 1y y' = \frac{x^x}{x} + \ln x(x\ln x)(\ln x + 1)\]
\[\Large y' = x^{x^x}[\frac{x^x}{x} + \ln x(x\ln x)(\ln x + 1)]\]

Answer 4

you have a mistake. according to you own work, you have
\[ \ln y=x^x\ \ln x \]
and worked on the side
\[ a=x^x \Rightarrow \ln a=x\ln x \Rightarrow a'=x^x(1+\ln x) \]