Having established the need for understanding change and optimization in machine learning, this chapter focuses on the simplest case: functions with a single input variable. We will begin with the concept of a limit, which provides the formal groundwork for defining the derivative.

You will learn how to calculate the derivative, representing the instantaneous rate of change or the slope of a function $f(x)$ at a specific point, often denoted as $f'(x)$ or $\frac{dy}{dx}$. We will cover standard differentiation rules (like the power rule, product rule, and quotient rule) necessary for finding derivatives of common functions.

A key application we will examine is using derivatives to locate the minimum and maximum points of a function. This is the starting point for understanding how optimization algorithms refine machine learning models. Finally, we will translate these mathematical concepts into practice by computing derivatives using Python libraries.