Page 2: Advanced Derivative Problems

This page continues with more sophisticated derivative problems, focusing on complex function combinations and applications.

Vocabulary: The notation y' represents the derivative of y with respect to x.

Example: Problem 7 shows y = x·e^x + x, demonstrating the product rule combined with exponential functions.

Highlight: Special attention is given to problems involving fractions and exponential terms.

The exercises incorporate multiple derivative rules simultaneously, requiring students to:

• Apply the product rule
• Handle exponential functions
• Work with fractional expressions
• Combine multiple derivative rules

Page 3: Elementary Derivative Table and Rules

This page presents a comprehensive reference of derivative rules and fundamental formulas.

Definition: Elementary functions are the basic building blocks of calculus, including constants, powers, exponentials, and logarithms.

Highlight: The table includes derivatives of all basic functions and operations, serving as a complete reference guide.

The page is organized into three main sections:

1. Elementary Function Derivatives
2. Operations with Derivatives
3. Composite Function Derivatives

Example: For exponential functions, f(x) = e^x has the derivative f'(x) = e^x, maintaining its form.

The material provides a structured approach to understanding and applying derivative rules in various mathematical contexts.

Page 1: Practice Exercises in Derivative Calculations

This page presents a collection of derivative calculation exercises designed to reinforce fundamental concepts in calculus.

Definition: A derivative represents the rate of change of a function at any given point.

Example: The derivative of y = 5x is y' = 5, demonstrating the power rule for linear functions.

Highlight: The exercises progress from simple linear functions to more complex expressions involving powers and logarithms.

The page contains twenty carefully selected problems that cover various types of functions, including:

• Linear functions
• Polynomial functions
• Logarithmic expressions
• Power functions
• Product combinations