Derivatives of composite functions/Derivatives of products and quotients (9/30/2008)

1. Main points

In today’s reading we learned how to find the derivative of a composite function by taking the derivative of the outside function times the derivative of the inside function, called the chain rule. To use this rule one must first rewrite the composite function using a new variable to represent the inside function. We also learn how to find the derivative of a product, which is the derivative of the first times the second, plus the first times the derivative of the second, this is the product rule. Lastly the derivative of a quotient, which is the derivative of the numerator times the denominator minus the numerator times the derivative of the denominator, all over the denominator squared, the quotient rule.

2. What was challenging

There was not a lot of hints in the book to why we use these rules which I would be very useful to be at least elementary be able to do. The examples you do in class to do this is much appreciated!

3. Interesting

I now have a deeper understanding of the many uses of a derivative within calculus and its many uses by learning these rules and how they are applied to make sense of the world around us.