Chapter 4  More Derivatives"Now that you have completed a chapter filled with derivative rules and their proofs, you are about to embark on another derivative chapter, this one devoted to a single rule: the Chain Rule. This rule certainly deserves its own chapter, but we also want you to become sufficiently familiar with the rich variety of applications that are accessible once you know how to apply it."
"You might think of Chapter 3 as the chapter that showed you how to make the bricks; now Chapter 4 will show you have to use those bricks to build houses." (Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. "Chapter 4." Calculus: Graphical, Numerical, Algebraic. 5th ed. N.p.: Pearson Education, n.d. 154. Print. AP Edition.) 
Chapter 4 reallife math connection.

Lesson 4.1  Chain Rule
This lesson will teach students to differentiate composite functions and parametrically defined functions using the Chain Rule. Lesson 4.2  Implicit Differentiation
This lesson will teach students to find derivatives of implicitly defined functions and thereby analyze parametrically defined curves. 
Lesson 4.3  Derivatives of Inverse Trigonometric Functions
This lesson will teach students to use implicit differentiation to find the derivatives of inverses of functions with known derivatives, including inverse trigonometric functions. Lesson 4.4  Derivatives of Exponential and Logarithmic Functions
This lesson will teach students to find derivatives of exponential functions and logarithmic functions with positive base a (a not equal to 1). 