1. Partial Derivatives and the Gradient

2. Definition of Partial Derivative

3. Geometric Interpretation (x 0,y 0 ) x y z Slope = f x (x 0,y 0 )

4. Geometric Interpretation x y z Slope = f y (x 0,y 0 ) (x 0,y 0 )

5. Evaluating Partial Derivatives from the Definition

6. Example

7. Definition of Partial Derivative

8. Leibniz’s Notation

9. Example

10. Examples

11. Example r R h

12. Mixed Partials

13. Example

14. Remark

15. Definition of Gradient

16. Example

18. Does Partial Differentiability Imply Continuity?

19. Gradient Formulas