Calculus through Data & Modeling: Differentiation Rules

In previous course, we defined and calculated the derivative as a limit. In this module, we will examine the derivatives of some important functions, including polynomials, exponentials, logarithms, and trigonometric functions. We will also learn differentiation rules which will help us to compute derivatives more efficiently. Finally, we will generalize the idea of a derivative to multivariable functions, and learn how to find derivatives and rates of change on a graph in space.

The formulas of this section enable us to differentiate new functions formed from old functions by multiplication or division.

Before starting this module, please review trigonometric functions, in particular their graphs. In this module, we will develop formulas to find derivatives for the common trigonometric functions of sine and cosine. Together with the product and quotient rules, the derivatives for the remaining trigonometric functions are formulated. These new derivative formulas are then added to our catalog to use and apply to solve problems related to rates of change.

Many functions are created through composition of other functions. In this module, one of the most important of the differentiation rules of this course is developed which will allow us to find derivatives of the compositions of functions. This rule is called the chain rule and has a variety of applications.