How to Differentiate ln(ln(ln x)) ?

What is the derivative of ln(ln(ln x))? This is a composite function that involves multiple functions within it. It contains a composite function inside a composite function. Therefore, solve this using Chain Rule Differentiation for a total of two times. First, differentiate the whole function. Then, multiply it by the derivative of the inner function. And repeat it for one more time.
CHAIN RULE EXPLANATION VIDEO: • Learn Chain Rule Diffe...
DERIVATIVE of ln(ln x): • How to Differentiate l...
DERIVATIVE of ln x: • How to Differentiate l...
0:00 Introduction
0:20 It's a Composite Function
0:46 Applying Chain Rule 1st time
1:32 Applying Chain Rule 2nd time
2:07 Multiply terms together
2:18 We did it!
2:28 Outro
#differentiation #chainrule #logarithm

[@anirudh_pranesh]

so easy. very simple derivative question. even babies can do this. why make video on this

[@YeahMathIsBoring]

You must have mastered differential calculus, making you feel that this question is extremely easy. I agree with you, it is indeed an easy and straightforward derivative question, involving the chain rule inside another chain rule. If you're wondering why I continue to make these videos, it's important to consider that not everyone is familiar with these types of questions. You might want to explore other videos that match your current level and understandings. I'll keep working on this and try to create more videos discussing related topics, especially for those who may be struggling with these questions.

[@anirudh_pranesh]

yes sorry. i appreciate your efforts@@YeahMathIsBoring

[@YeahMathIsBoring]

@@anirudh_pranesh It's okay. Thanks anyway!

[@user-ky5dy5hl4d]

To simplify one can for final answer: 1/xln(lnx^2)

[@Xaike69]

What do you think about serge lang calc books? 🤔

[@YeahMathIsBoring]

I'm afraid that I couldn't offer an opinion on the book as it's unfamiliar to me. However, it seems like a promising option if you're aiming to learn calculus from the basics.

[@adityadeodhar8819]

lawn x fr

[@MagnificentCreature]

Oh I can’t wait for the derivative of ln(ln(ln(ln(x))))

[@YeahMathIsBoring]

Sure! Then I'll be making for that soon

[@idkyet9458]

d/dx ln(f(x)) = f'(x)/f(x)
so d/dx ln(ln(lnx)) = (1/xlnx)/ln(lnx)) = 1/(xlnx)(ln(lnx))

[@YeahMathIsBoring]

Exactly! According to the chain rule, it'd be 1/f(x) multiply by f'(x), which results in f'(x)/f(x), and finally arrives to that answer. Well done! You have a great understanding on this!

[@idkyet9458]

@@YeahMathIsBoring therefore,
d/dx ln(ln(ln(ln(ln(ln(ln(ln(ln(lnx))))))))) = 1/(xlnx)(ln(lnx))(ln(ln(lnx)))(ln(ln(ln(lnx))))(ln(ln(ln(ln(lnx)))))(ln(ln(ln(ln(ln(lnx))))))(ln(ln(ln(ln(ln(ln(lnx)))))))(ln(ln(ln(ln(ln(ln(ln(lnx))))))))(ln(ln(ln(ln(ln(ln(ln(ln(lnx)))))))))

[@YeahMathIsBoring]

@@idkyet9458 Absolutely!