Can Anyone Help Me Solve Derivative x^x^x with Additional X?

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Discussion Overview

The discussion revolves around finding the derivative of the expression x^(x^x), with participants exploring different interpretations and methods for differentiation. The scope includes mathematical reasoning and technical explanations related to derivatives.

Discussion Character

  • Mathematical reasoning, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion about differentiating x^(x^x) and seeks assistance.
  • Another participant clarifies the expression by asking whether it is (x^x)^x or x^(x^x), assuming the former initially.
  • After clarification, a participant suggests using the natural logarithm and the product rule to differentiate x^(x^x), indicating familiarity with the derivative of xx.
  • A different participant questions the feasibility of differentiating (x^x)^x, suggesting it seems impossible, but another responds by demonstrating that it can be rewritten as x^(x^2) and provides a differentiation approach using the chain rule.
  • A reminder is issued not to re-open old threads, indicating a concern about the longevity of the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the difficulty of differentiating (x^x)^x, with some asserting it is possible while others express skepticism.

Contextual Notes

There are unresolved assumptions regarding the methods for differentiation and the interpretations of the expressions involved. The discussion also highlights the potential for confusion in notation and mathematical operations.

Who May Find This Useful

Readers interested in advanced calculus, particularly in differentiation techniques for complex exponential expressions, may find this discussion relevant.

silence
i can solve x^x but adding this new x just confuses me any help will do, X^x^x
 
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Do you mean (x^x)^x or x^(x^x)? I'm assuming the former.
 
sorry i meant x^(x^x)
 
Glad you picked that one. Get something like ln(y) = xxln(x) and use the product rule. Don't forget you already know d(xx)/dx :wink:
 
wow i never noticed that i was doing it a long way which would have come out wrong anyways. thanks for the help
 
ok ok
 
Last edited:
djuiceholder said:
but can you do (x^x)^x ??
it seems impossible

1. It is not at all imposible; note that this equals: (x^{x})^{x}=x^{x^{2}}
Rewriting this as:
x^{x^{2}}=e^{x^{2}\ln(x)}
We may readily differentate this by means of the chain rule, yielding the derivative:
x^{x^{2}}(2x\ln(x)+x)

2. Please do not re-open nearly 6-year old threads.
 
ok ok
 
Last edited:

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