Differentiate x^x and analyze domain
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
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, ∞).
Quick Answer: 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.
