derivative brain teaser

[BMAD]

let a = ln(ln(x))/(ln(x)

let b= x^a

let y = e^b

find dy/dx

[bonanova]

Spoiler

Spoiler

 

 

But seriously, working on it.

 

 

[bonanova]

Looks like ...

Spoiler

dy/dx = 1

Spoiler

b = x^a = e^{a ln x} = e^{ln ln x} = ln x
y = e^b = e^{ln x} = x

 

 

Edited March 12, 2018 by bonanova
Further simplification