1. 3.1 Derivatives
Part 2

2. is called the derivative of at .
We write:
“The derivative of f with respect to x is …”
There are two formulas for the derivative of

3.   The Definition of the Derivative: y2 y1 x2 x1
The Derivative at a Point:  x2 x1
There are many ways to write the derivative of

4. “the derivative of f with respect to x”
“f prime x” or
“y prime”
“the derivative of y with respect to x”
“dee why dee ecks” or
“the derivative of f with respect to x”
“dee eff dee ecks” or
“the derivative of f of x”
“dee dee ecks uv eff uv ecks” or

5. Note:
dx does not mean d times x !
dy does not mean d times y !

6. Note: does not mean ! does not mean !
(except when it is convenient to think of it as division.)
does not mean !
(except when it is convenient to think of it as division.)

7. Note: does not mean times !
(except when it is convenient to treat it that way.)

9. The derivative is the slope of the original function.
The derivative is defined at the end points of a function on a closed interval.

10. The derivative is the slope of the original function.
f (x)
f ´(x)

11. A function is differentiable if it has a derivative everywhere in its domain. It must be continuous and smooth. Functions on closed intervals must have one-sided derivatives defined at the end points. p