Basic Rules of Differentiation (Part 2)

In Part 1, we learned two basic rules that allow us to differentiate polynomial functions. Now we will learn to deal with functions that involve the multiplication or division of functions. We will learn about product rule and quotient rule.

Product Rule:

Suppose we have a function f(x) that is the result of the multiplication (known as a product) between two functions g(x) and h(x). Then, the derivative of f(x) is given by:

Many teachers and students play with words to memorize this rule. Anyone can make up his/her own way to remember it, but it basically says the derivative of f(x) is "the first times derivative of the last, plus the last times derivative of the first."

Quotient Rule:

Suppose we have a function f(x) that is the result of the division (known as a quotient) of the functions g(x) by h(x). Then, the derivative of f(x) is given by:

In this case, we can say the derivative of f(x) is "the bottom times derivative of the top, minus the top times derivative of the bottom. All divided by the bottom squared."

Examples:

These two rules are quite popular, so let's look at some examples. Notice that we will apply the rules learned in Part 1 when dealing with the terms of the functions.

Now, as seen in the examples, we can differentiate more complicated functions!!!