Computing Derivatives Introduction
We've already been through the formal derivative definition. Sure, it's fun to be formal once in a while. Have a meal way better than the cafeteria offers. Maybe hop a ride in a limo...eat with a knife and fork. Seriously, who wants to do that everyday? It's time to cut loose (footloose?). Even better, it's time to cut some calculus corners. In this section we'll discuss the cheat codes...or rules...for computing derivatives. The rules allow us to skip ahead of the level that uses limits, into the level where more complicated functions can be conquered. There are rules for many different function scenarios, so learn them and be a calc champ.
When we compute derivatives, we're mostly doing mechanical computations. After we've learned all the rules and have practiced enough, we'll be able to compute the derivatives of most functions we'll encounter almost without thinking. Of course there are reasons along with the rules, and understanding the reasons will probably make memorizing the rules more...memorable.