1. Composition of Functions: The process of combining two or more functions in order to create another function. One function is evaluated at a value of the independent variable and the result is substituted into the other function as the independent variable. The composition of functions f and g is written as: 1.7 – The Chain Rule The composition of functions is a function inside another function.

2. 1.7 – The Chain Rule

4. Review of the Product Rule: and are composite functions.

5. Additional Problems: 1.7 – The Chain Rule

9. a) b)

10. 1.8 –Higher-Order Derivatives Higher-order derivatives provide a method to examine how a rate-of-change changes. Notations

11. 1.8 –Higher-Order Derivatives Find the requested higher-order derivatives.

12. 1.8 –Higher-Order Derivatives Velocity: the change in position with respect to a change in time. It is a rate of change with direction. Position, Velocity, and Acceleration

13. 1.8 –Higher-Order Derivatives Velocity: the change in position with respect to a change in time. It is a rate of change with direction. Position, Velocity, and Acceleration

14. Acceleration: the change in velocity with respect to a change in time. It is a rate of change with direction. 1.8 –Higher-Order Derivatives

15. a) b) 1.8 –Higher-Order Derivatives feet/sec/sec

16. 1.8 –Higher-Order Derivatives The position of a particle (in inches) moving along the x-axis after t seconds have elapsed is given by the following equation: s(t) = t 4 – 2t 3 – 4t 2 + 12t. (a) Calculate the velocity of the particle at time t. (b) Compute the particle's velocity at t = 1, 2, and 4 seconds. (c) Calculate the acceleration of the particle after 4 seconds. (d) When is the particle at rest? a) b) c) d)