- Topics At a Glance
- Derivatives of Basic Functions
- Constant Functions
- Lines
- Power Functions
- Exponential Functions
- Logarithmic Functions
- Trigonometric Functions
- Derivatives of More Complicated Functions
- Derivative of a Constant Multiple of a Function
- Multiplication by -1
- Fractions With a Constant Denominator
- More Derivatives of Logarithms
- Derivative of a Sum (or Difference) of Functions
- Derivative of a Product of Functions
- Derivative of a Quotient of Functions
- Derivatives of Those Other Trig Functions
**Solving Derivatives**- Using the Correct Rule(s)
- Giving the Correct Answers
- Derivatives of Even More Complicated Functions
- The Chain Rule
- Re-Constructing the Quotient Rule
- Derivative of a
^{x} - Derivative of
*ln*x - Derivatives of Inverse Trigonometric Functions
- The Chain Rule in Leibniz Notation
- Patterns
- Thinking Backwards
- Implicit Differentiation
- Computing Derivatives Using Implicit Differentiation
- Using Leibniz Notation
- Using Lagrange Notation
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

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. This will help to

- 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.