Differentiate x^x and analyze domain
Overview
This question evaluates proficiency with calculus concepts such as logarithmic differentiation, differentiation of variable-exponent functions, limit evaluation near domain boundaries, and identification of critical points.
Capital One
Oct 13, 2025, 9:49 PM
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Compute the derivative of f(x) = x^x for x > 0 using logarithmic differentiation. State precisely the domain where the derivative is real-valued. Evaluate lim_{x→0+} x^x and f′(1). Briefly discuss whether f(x) = x^x has any critical points on (0, ∞).