Make a list of all definitions in the section (a few words each is fine). Summarize any lengthy definitions introduced in this section in your own words.
derivative of a function f at a - denoted by 
,
provided the limit exists (that's right - this is exactly the same as the slope of the tangent line from section 2.6!). So the derivative of a function f at a point a is the slope of the tangent line to the curve at P(a,f(a)).
Alternatively, it can be considered the instantaneous rate of change of y=f(x) with respect to x when x=a.
Make a list of all theorems (lemmas, corollaries) in the section (a few words each is fine). Summarize each one introduced in this section in your own words.
None appeared to my eyes.
Make a note of any especially useful properties, tricks, hints, or other materials.
Sometimes the derivative is merely estimated from data, using average rates of change, or by a visual approximation based on a graph.
Summarize the section in two or three sentences.
This section is an easy extension of section 2.6: the big picture is that the dreaded derivative, one of the fundamental concepts of calculus, is actually just the same as the slope of a tangent line to a curve. It can also be considered an instantaneous rate of change.