Question

Use logarithmic differentiation to find the derivative

Answer 1

\[f(x)=(\ln x)^{\ln x}\]

Answer 2

what's the first step of logarithmic differentiation?

Answer 3

cry

Answer 4

loll...hint: it has to do with taking the logarithm of the expression

Answer 5

\[\frac{ d }{ dx }(\ln x)=\frac{ 1 }{ x}\]

Answer 6

uhm. You're going to need this rule, but you gotta be able to rewrite your expression into something you can handle first

Answer 7

Ooo fun problem :)

Answer 8

What's the trick? Just walk through it. Introduce the logarithm and go!

Answer 9

This feels like this weird thing where a power of logarithms can swallow itself haha: \[\LARGE \ln^2(x)=\ln(x)*\ln(x)=\ln(x^{lnx})\]