Derivatives%20by%20Definition

1
Derivatives by Definition

• The Long Way
• (no shortcuts!!)

2
Definition

• The derivative is the slope of a curve at a
  point.
• Notation y f(x)

3
The Theory

• If Q slides really close to P, then the slope of
  the secant line becomes very very close to the
  slope of the tangent line. What do I mean??

Q
Q
Q
P
P
4
What is the formula?

• Since its a slope equation, its based on
• If we take the limit as h gets very very small
• (h being the x distance between P and Q)
• we get

5
The Definition of a Derivative
6
Examples