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The derivative of x^x involves using logarithmic differentiation.
Apply logarithmic differentiation: y = x^x = e^(xlnx)
Take the natural logarithm of both sides: ln(y) = xlnx
Differentiate both sides with respect to x: (1/y) * dy/dx = ln(x) + 1
Substitute back y = x^x to find dy/dx
The derivative of x^x is x^x(1+logx).
Use the chain rule to differentiate x^x
Apply logarithmic differentiation to find the derivative
The derivative of x^x is x^x(1+logx)
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