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Question:
What is the derivative of x^x and x^x^x.
Is there a generalised form for the derivative of x tetrated to n. i.e. the derivative of the power tower of order n for x.

Step-by-step walkthrough of the variations of a popular technical interview question involving the derivative of x^x. Variations include x^x^x and deriving and proving a general form for the derivative. This is known as the tetration operation. Find the derivative of x tetrated to 2 and x tetrated to 3.

This question is suitable as practice for Quant Trading, Quantitative Researcher, Quantitative Developer, Desk Quant and Data Scientist technical interviews

Timestamps:
0:53 - Derivative x^x, power tower of order 2 - Method 1
2:13 - Derivative x^x, power tower of order 2 - Method 2
3:18 - Derivative x^x^x, power tower of order 3 - Method 1
4:38 - Derivative x^x^x, power tower of order 3 - Method 2
5:44 - The Tetration operation, what is it and why we don't know it
7:58 - Derivative x^x^x^x^x...n , power tower of order n - Generalised Form
14:44 - Derivative x^x^x^x^x...n , Proof by Induction
18:38 - Generalised Form Function Domain

Free Resources:
Free Excel List of Firms Google Drive: https://shorturl.at/vMUX8

Question Source:
Question 16 of “An Interview Primer for Quantitative Finance" - Dirk Bester

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