Part 1/5:

Understanding the Derivative of Power Functions

In the world of calculus, power functions represent a core concept essential for understanding derivatives. The focus of this discussion is on the derivative of power functions, especially for cases where ( n ) is a positive integer. Through various examples, we’ll explore the derivative of simple power functions and recognize overall patterns that emerge.

The Basics of Power Functions

A power function can be generally expressed as ( f(x) = x^n ), where ( n ) is a positive integer. The simplest instance of this function is when ( n = 1 ), giving us ( f(x) = x ).