Today we discussed our first “short cut” to find instantaneous rates of change.  We reviewed the basic rule.  While we applied the rule to some routine problem which were already in the x^n format, we quickly moved to problems which had to be rewritten into the appropriate form.  We multiplied quantities out.  We simplified rational expressions.  We rewrote fractions from terms such as sqrt(x) to x^(1/2).

**Even though it may see backwards to learn the Power Rule before spending time fully developing the definitions of derivatives, we are learning the Power Rule first to allow us to check our answers when finding derivatives using our formal limit definitions. **

We also spent part of the period reviewing the ideas of AROC (average rate of change – slope of a secant line) and IROC (instantaneous rate of change – slope of the tangent line).  We will discuss three variations on these limit definitions over the next few days.