Posted: Feb 24, 2012 9:03 am
QUOTIENT RULE

The quotient rule is about two functions that are divided with each other: so given two functions, f(x) and g(x) that are being divided, how do we differentiate?

The derivative will be:

Using words: the derivative of two functions being divided is given by the derivative of the numerator times the denominator, minus the numerator times the derivative of the denominator; all this divided by the square of the denominator. Sounds complicated right? However, once you practice it a bit, it will be very easy to do. Let's see a simple example:

In the above we have:

When we differentiate the above two we get:

How about the square of the denominator?

Then let us apply the rule as above:

The quotient rule takes some practice. But it is not as difficult as it may seem at first glance. Tomorrow I will finish up with the composite rule; I wanted to do it today, but explaining the quotient rule I saw that it may be better to do the last rule tomorrow, and let you read and understand the quotient rule first.