1. Various Symbols for the Derivative

2. Figure 6-2(a). Piecewise Linear Function (Continuous).

3. Figure 6-2(b). Piecewise Linear Function (Finite Discontinuities).

4. Piecewise Linear Segment

5. Slope of a Piecewise Linear Segment

6. Example 6-1. Plot the first derivative of the function shown below.

8. Development of a Simple Derivative

9. Development of a Simple Derivative Continuation

10. Chain Rule
where

11. Example 6-2. Approximate the derivative of y=x2 at x=1 by forming small changes.

12. Example 6-3. The derivative of sin u with respect to u is given below.
Use the chain rule to find the derivative with respect to x of

13. Example 6-3. Continuation.

14. Table 6-1. Derivatives

15. Table 6-1. Derivatives (Continued)

16. Example 6-4. Determine dy/dx for the function shown below.

17. Example 6-4. Continuation.

18. Example 6-5. Determine dy/dx for the function shown below.

19. Example 6-6. Determine dy/dx for the function shown below.

20. Higher-Order Derivatives

21. Example 6-7. Determine the 2nd derivative with respect to x of the function below.

22. Displacement, Velocity, and Acceleration