Differential And Integral Calculus By Feliciano And Uy Chapter 4 < Updated | 2025 >

To use the first and second derivatives to analyze the behavior of functions, sketch their graphs accurately, and solve real-world optimization problems.

By the end of this chapter, you should be able to derive trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) and solve basic application problems (slopes, rates of change, velocity). To use the first and second derivatives to

Though sometimes treated as a separate advanced topic, many standard texts, including Feliciano and Uy, introduce implicit differentiation in the context of the Chain Rule. This technique is used when a function is not isolated as $y = f(x)$. By the end of this chapter, you should

In the study of calculus, the derivative represents the instantaneous rate of change of a function. While the definition of the derivative—derived from the concept of limits—is foundational, it is computationally cumbersome for complex functions. Feliciano and Uy dedicate Chapter 4 to streamlining this process. The chapter introduces a set of algebraic rules that allow for the differentiation of functions without resorting to the lengthy process of evaluating limits of difference quotients. Mastery of these rules is prerequisite for applications such as curve sketching, optimization, and related rates found in subsequent chapters. By the end of this chapter