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

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The discussion centers on solving the derivative of the expression x^(x^x), which is clarified to be the correct interpretation. Participants suggest using logarithmic differentiation, specifically ln(y) = xxln(x), and applying the product rule for differentiation. The conversation also touches on the derivative of (x^x)^x, which simplifies to x^(x^2) and can be differentiated using the chain rule. The importance of avoiding reopening old threads is noted at the end. Overall, the thread provides insights into differentiating complex exponential expressions.
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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