Power Functions: Definition

This lecture covers the generalization of powers where both the exponent and the base are functions, using the concepts of exponential and logarithmic functions. By defining and studying x*, the lecture explores the behavior of power functions in different limits, emphasizing the continuity of the exponential function. The lecture also delves into the derivative of x ln(x) to analyze the behavior of power functions in various intervals. Through the study of f(x) = x ln(x), the lecture demonstrates how to determine the behavior of exponential functions. The lecture concludes with the generalization of power functions and the derivability of fª in different scenarios.