The linear nature of graphs
UBC Calculus Online Course Notes

Introduction to Derivatives

"O, rocks! Tell us in plain words."
--Mrs. Marion Bloom, Ulysses by James Joyce

Now that we've seen many different functions, it's time to turn our attention to the central notion of this course---the derivative. This is the key to deepening our discussion about functions.

The derivative is one of the greatest ideas that we as humans have created to describe our natural world. It took thousands of years for the idea to be formulated in a way which is really useful (so don't be discouraged if it takes you a day or two!).

As with any great idea, the derivative may be considered from several different perspectives. However, they all boil down to this:

The derivative tells us how to approximate a graph, near some base point, by a straight line.

In this section, we want to give you a feel for what the derivative is from a few of these perspectives and what kind of information it measures. Later on, we'll learn how to actually compute with this notion, but let's not worry about that now.