Proofs- To be, or not to be?

Hello, Readers!

I have a question for you guys, as well as some news!

Firstly, I want to let you guys know about some news! Fairly soon (possibly tomorrow, but by the end of next week for sure), I am going to redesign the website to it’s permanent form. I want to create some new links, new pages, new categories, and a new overall design! Maybe even a cool logo! The aesthetics are pretty important to a website, as I want it to look professional and user-friendly. If there is anything that you think would improve the website, please let me know! Comment below with any feedback, advice, ect.

More importantly than the website design, I have a question for anyone who will listen. Would anyone benefit from a category about proofs? In my lessons, I have and will continue to provide small, abbreviated proofs/reasons for why things are how they are. If you would like, I can create a category that gives the fully detailed proof of how everything works. This category will not be my highest priority, but I could definitely make posts like that if it would be helpful to anyone. Would it be useful to you? For me, personally, I like to know the proofs. But, hey, I’m a math geek, so how do I know what the rest of the world likes? =)

Comment below please for suggestions, advice, or any type of feedback! Anything is appreciated.

What is the derivative of x^(x^(x^(x^…)))?

This question was submitted by @NestorAiros via Twitter. Thank you, Nestor! You have certainly come to the right place for your math questions! Congratulations on being the very first user question!

Actual Question:
“@CalculusTricks hey bro! Idon’t speak lot of english but here is myquestion,hope u understand: how i do differiancibility: y=x^x^x .. y’=?”

Your english is good! Very understandable.

What is the derivative of ?

Remember that  .

Let’s take this on step at a time. Maybe we can find a pattern. First, simplify the problem. What is the derivative of ?

Use implicit differentiation.

Now, what about ?

That is as far as this one simplifies. The next couple are going to get much, much messier. But I’ll  do out one more completely.

Let’s find the derivative of !

See? Messy. This starts to get quite tedious, so I am just going to post the solutions to the next few steps.

It took me a bit to figure out what the pattern was, but there is one! Try writing all of them on paper, and you can see it much better. Then, you can imply the answers for any following steps in this problem. I really hope this answers your question. Please let me know either way by commenting below. If you have further questions, email me at admin@calculustricks.com. I will reply to you via email, and update this post if necessary.

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