How to Differentiate ln(ln x)?

What is the derivative of ln(ln x)? This is a composite function. Supposed that we have ln x, but for now we have ln(ln x) instead. Therefore, solve this using Chain Rule Differentiation. First, differentiate the whole function. Then, multiply it by the derivative of the inner function.
Chain Rule of Logarithmic Derivative:
d/dx (ln f(x)) = (1 / f(x) ) * f'(x)
CHAIN RULE EXPLANATION VIDEO:
• Learn Chain Rule Diffe...
Derivative of (ln x): • How to Differentiate l...
0:00 Introduction
0:19 Composite Function
0:57 Using Chain Rule
1:30 We did it!
#differentiation #chainrule #logarithm

[@artemis_furrson]

My mind immediately jumped to applying the chain rule, but I thought it was a trick question and that the chain rule wasn't complete or something

[@YeahMathIsBoring]

It's just literally a normal chain rule. It is actually a simple question if we solve it part by part.

[@kenseyder]

In my country, calculus is taught at university, but I learned calculus (derivatives, integrals, limits) by myself in the 9th grade. Now I'm 10. And I could solve this problem without looking at the explanation 😄

[@YeahMathIsBoring]

That's great to hear! It's impressive that you took the initiative to learn calculus on your own in the 9th grade and that you can solve problems without needing additional explanations. Well done! Keep up the good job!

[@kenseyder]

@@YeahMathIsBoring Thank you very much ❤️

[@YeahMathIsBoring]

@@kenseyder You're welcome!

[@o0QuAdSh0t0o]

One over Lawn-X

[@YeahMathIsBoring]

Yeah, the derivative of ln x is indeed 1/x. For the derivative of ln(ln x), we apply the chain rule by first taking the derivative of the outer function and multiply by derivative of inner function. We got 1/(x ln x) as the final answer.

[@KartikPatel-nt4ff]

😅😅😅well information good show you 😅😅

[@Calcungruity]

Math ain't boring.. math is fun❤❤

[@YeahMathIsBoring]

Yup! You're right!

[@abhirupkundu2778]

ok? Once you solve competitive level questions in maths u are gonna cry bro