Having established what functions are and how limits describe their behavior near a point, we now turn to measuring how functions change. This chapter introduces the derivative, a concept used to find the instantaneous rate of change of a function. Understanding derivatives is necessary for optimizing machine learning models.

You will learn:

• The difference between average and instantaneous rates of change.
• The definition of a derivative as the slope of a tangent line to a function's graph.
• Common notations for derivatives, such as $f'(x)$ and $\frac{dy}{dx}$.
• Basic rules for calculating derivatives, including the power rule, constant rule, and sum rule.
• The idea of higher-order derivatives.

We will start with the intuition behind rates of change and build up to calculating derivatives for simple functions, providing practice along the way. This forms the groundwork for using calculus in optimization later in the course.