We started by looking at extrema for functions, maxima and minima. They can be seen on graphs with a flat slope and can also be calculated by using the first derivative.
We looked at derivatives of some trigonometric functions including arc sine as well as the domain of the functions. It can help to look at the functions in a few ways. Two ways are on a unit circle and also as an oscillating function on the x-y graph.
U-substitution is a useful approach and includes the chain rule. I actually have a table of derivatives that uses u each time. That can be a good way to think about derivatives since many times there will be something other than x that is being operated on by the function.