You must commit this table to memory.

We could give each of these a name. In order, we will refer to them as the power rule, exponential rule, log rule, sine rule and cosine rule. You should be aware that other authors will have a different list of elementary functions. For example, we could add the other four trig functions to the list. We will see how to get those derivatives from these starting in the next lecture. I am going to focus on the structure of the computations so that you will be able to add whatever you need in the future.

What I want to emphasize in the following lectures is a very important concept referred to in general as analysis. In this context, analysis is applied as follows. We now know the derivatives of the elementary functions. More than likely, the functions that we will need to model real world systems will not be elementary and we will want to know their derivatives - i.e. their rates of change. In a previous lesson we learned how to take a function apart into its elementary pieces. We also kept track of the operations that were used to put these elementary functions together to get the original function. So if we know the derivatives of the elementary functions its reasonable to assume that we can get the derivatives of the more complicated functions from these. That is if we knew how to put the derivatives together to get the derivative of the function that we started with. That process of putting the derivatives together is exactly what we will learn to do in the following lectures. Let me warn you at this point that the derivatives do not necessarily go back together the way that the function came apart. However, once we know which elementary functions are involved and which operations are used we will be able put the derivatives of the elementary functions together in a consistent and well defined way to get the derivative of the function. You will see what this means soon enough.