- 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

The first kind of function is a constant function.

If *f*(*x*) = *C* for some constant *C*, then *f'*(*x*) = 0.

Constant functions have a slope of zero. On a graph, a constant function is a straight vertical line. It doesn't matter if we pick *f*(*x*) = 3 or *f*(*x*) = -10, or *f*(*x*) = π, or any other constant, the result would be the same. Zero. We like.

Exercise 1

What is the derivative of the function *f*(*x*) = 5?