The Chain Rule

Most of the function students are faced with in beginning calculus are compositions of the Elementary Functions. The Chain Rule allows you to differentiate composite functions easily. The posts listed below are ways to introduce and use the Chain Rule. Experimenting with a CAS – Chain Rule  Using a CAS to discover the Chain Rule…

Derivative Formulae

So, no one wants to do complicated limits to find derivatives. There are easier ways of course. There are a number of quick ways (rules, formulas) for finding derivatives of the Elementary Functions and their compositions. Here are some ways to introduce these rules; these are the subject of this week’s review of past posts. Why…

Implicit Differentiation

I discovered in doing next week’s post that I apparently never wrote about implicit differentiation. So here goes – an extra post this week! Implicit Differentiation The technique of implicit differentiation allows you to find slopes of relations given by equations that are not written as functions, or may even be impossible to write as…

The Chain Rule

Most of the function students are faced with in beginning calculus are compositions of the Elementary Functions. The Chain Rule allows you to differentiate composite functions easily. The posted listed below are ways to introduce and then use the Chain Rule. Experimenting with a CAS – Chain Rule  Using a CAS to discover the Chain…

Differentiation Techniques

So, no one wants to do complicated limits to find derivatives. There are easier ways of course. There are a number of quick ways (rules, formulas) for finding derivatives of the Elementary Functions and their compositions. Here are some ways to introduce these rules; these are the subject of this week’s review of past posts. Why…

Working up to the derivative.

While limit is what makes all of the calculus work, people usually think of calculus as starting with the derivative. The first problem in calculus is finding the slope of a line tangent to a graph at a point and then writing the equation of that tangent line. Local Linearity is the graphical manifestation of…

Tangent Lines

Second in the Graphing Calculator/Technology series This graphing calculator activity is a way to introduce the idea if the slope of the tangent line as the limit of the slope of a secant line. In it, students will write the equation of a secant line through two very close points. They will then compare their…