# Instantaneous Rate of Change — Lecture 8. The Derivative.

The **derivative** of a **function** y = f(x) is the **function** deﬁned by f0(x) = lim h→0 f(x+h)−f(x) h. So the **derivative** f0(x) of a **function** y = f(x) spews out the slope of the tangent to the graph y = f(x) at each x in the domain of f where there is a tangent line. One thing we will have to deal with is

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