1. Limits, continuity, and differentiability computing derivatives

2. Today in Review (show all work):
Limits and Continuity Class Work: #1-7 Derivatives Class Work: #1-8, 22
Limits and Continuity Homework: #8-26 Derivatives Homework: #9-21, 23-26

3. Card 2: Techniques for limits
Graphically
Numerically (table)
Algebraically (Direct Substitution, Rationalize, Factor, Simplify Complex Fraction, Distribute/Expand, Trig Manipulation)
Card 2: Techniques for limits

4. Card 3: L’hopital’s rule

5. Card 4: differentiability
Note: A function is not differentiable at a: sharp turn, corner, cusp, vertical tangent line
Note: If a function is differentiable, then it is continuous (but the converse is not necessarily true!)

6. Card 5: definition of a derivative

7. Card 6: Power, product, quotient, chain rules

8. Card 7: derivatives of trig functions

9. Card 8: derivatives of inverse trig

10. Card 9: derivatives of logs & exponentials

11. Card 10: implicit differentiation
Steps:
Take the derivative of both sides with respect to x
Collect all dy/dx terms on one side
Factor out dy/dx
Solve for dy/dx

12. Card 11: derivative of an inverse function