Unit 3: The Derivative
A. Definition of the derivative
Derivatives Practice Quiz (definition and concept)
B. Differentiability
1. Local linearity
2. Numeric derivatives using the calculator
3. Differentiability and continuity
C. Secant and tangent lines (average versus instantaneous rate of change)
D. Techniques of differentiation
1. Notation
2. Derivatives of polynomial functions
3. Derivatives of trigonometric functions
4. Derivatives of radical functions
E. Derivative rules when combining functions
Guided Notes to Follow Videos (PDF)
Solutions to NOTES from Videos (PDF)
Problems to try on your own (PDF)
1. Power rule
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video) Example 5 (Video)Example 6 (Video) Example 7 (Video) Example 8 (Video) Example 9 (Video)
2. Product Rules
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video)
Example 5 (Video) Example 6 (Video) Example 7 (Video) Example 8 (Video)
3. Quotient Rule
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video)
Example 5 (Video) Example 6 (Video) Example 7 (Video)
4. Chain Rule (Applied across all the rules)
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video) Example 5 (Video)Example 6 (Video) Example 7 (Video) Example 8 (Video) Example 9 (Video)
F. Implicit derivatives
G. Normal lines
H. Related rates
I. Derivatives of logarithmic and exponential functions
Calculus Review of Derivatives