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

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SUMMARY

The derivative of the function X^(x^x) can be computed using the chain rule. By letting t = x^x, the derivative can be expressed as d/dx(X^t). The established method involves differentiating X^t with respect to x, applying the chain rule effectively. This approach leverages the known derivative of X^x to simplify the process.

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Homework Statement


I uploaded a image file of the question.


Homework Equations


I've seen the derivative of X^x but how do I do this one?


The Attempt at a Solution

 

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Put t=xx and apply the chain rule since you know what d/dx(xsup]x[/sup]) gives.
 

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