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The formula for the derivative of x^(x^x) is (x^x)*(1+ln(x)+ln(x^x)).
To find the derivative of x^(x^x), you can use the chain rule and the product rule. First, rewrite the function as e^(x^x*ln(x)). Then, use the chain rule to find the derivative of x^x*ln(x), which is x^x*(1+ln(x)). Finally, use the product rule to find the derivative of e^(x^x*ln(x)), which is (x^x)*(1+ln(x)+ln(x^x)).
No, the derivative of x^(x^x) is not defined for all values of x. It is undefined when x=0, and it does not exist at negative values of x.
The graph of the derivative of x^(x^x) is a curve that starts at (0,1) and approaches 0 as x increases. It has a vertical asymptote at x=0 and is undefined for negative values of x.
Yes, the derivative of x^(x^x) can be simplified further to (x^x)*(1+ln(x)+2ln(x^x)). This can be rewritten as (x^x)*(1+3ln(x)).