There are a lot of rules floating about now. Besides knowing how to take the derivatives of less complicated functions, we have all these rules for taking the derivatives of more complicated functions:
These rules can be combined in all sorts of ways. How do we know which one(s) to use?
There are several parts to the answer,
- Practice. Every derivative calculated helps our sense of what we should be doing to find that next derivative.
- Keep track of the work carefully, like we did when finding the derivative of a product of 3 functions.
- Rewrite functions before finding derivatives.
- Find derivatives the simplest way - for example, use the multiplication-by-a-constant rule instead of the quotient rule
to find the derivative of .
- Work from the outside in. We haven't talked about this yet, but we will.