May 5 - Shortcuts to the Derivative

If the main concept yesterday (Tuesday) was the definition of the derivative, today's main idea was how to best calculate a derivative. It is important that you always keep in mind that the derivative is defined to be the limit of the slope between points, but we will rarely (never) use the limit definition to find the derivative of a function.

For now it's all about the Power Rule. Examples are included of how to apply the Power Rule even when it isn't immediately obvious.

Thanks again to Rachel for providing her notes for today.

May 4 - Slope of a curve

The main concept for today was the definition of the derivative. Imagine two points on a curve - call them (x, f(x)) and (c, f(c)). Calculate the slope between those points (change in y over change in x) and then take the limit of that expression as x -> c (which implies that the two points "move" ever closer together). The value of the limit can be interpreted as the slope at that point (c, f(c)).

Thanks to Rachel for her notes for today.