Differential And Integral Calculus By Feliciano And Uy Chapter 4 |best| Jun 2026

Chapter 4 of Differential and Integral Calculus by Feliciano and Uy serves as the bridge between the conceptual understanding of limits and the algorithmic application of differentiation. While previous chapters establish the definition of the derivative via limits, Chapter 4 focuses on the rules of differentiation. This paper summarizes the core concepts presented in the chapter, including the differentiation of algebraic functions, the Chain Rule for composite functions, and the fundamental theorems governing polynomials and rational expressions. The objective is to provide a structured overview of the theorems and formulas essential for solving computational problems in calculus.

A spherical balloon is being inflated so that its volume increases at a rate of $20\text cm^3/\texts$. How fast is the radius increasing when the radius is $5\text cm$? Step 1: Identify given rates and quantities. Given: $\fracdVdt = 20\text cm^3/\texts$ Find: $\fracdrdt$ when $r = 5\text cm$

From a 12×12 square, cut equal squares from corners, fold to make box. Maximize volume. (V = x(12-2x)^2), (V' = 0) → (x=2) (max), (x=6) (min)

They illustrate how to use derivatives to solve these problems. Chapter 4 of Differential and Integral Calculus by

4. Logarithmic and Exponential Functions (Sections 4.4–4.8) Feliciano and Uy transition to Euler's number ( ) using the classic limit theorem:

Using logarithmic differentiation for functions where the variable appears in both the base and the exponent.

A key emphasis in this section is mastering the (often represented as The objective is to provide a structured overview

Constants can be pulled out in front of the derivative operation. Sum and Difference Rules: The derivative of a sum is the sum of the derivatives. 2. Advanced Algebraic Rules

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(f(x) = x^4 - 4x^2) (f'(x) = 4x^3 - 8x = 4x(x^2 - 2)) → CP: (x = 0, \pm\sqrt2) (f''(x) = 12x^2 - 8) Step 1: Identify given rates and quantities

Transform the integral into terms of

A rectangular field is to be fenced off along a straight river bank (no fence is needed along the river). If the total length of the fencing material available is 120 meters, find the dimensions that maximize the enclosed area.

Identify trigonometric components that approach indeterminate forms ( 000 over 0 end-fraction