Derivadas usando la definición | Introducción
Introduction to Derivatives
In this section, the instructor introduces the concept of derivatives and provides an overview of the definition of derivatives.
Definition of Derivative
- The derivative is defined as the limit as h approaches 0 of (f(x + h) - f(x)) / h.
- Some books use "delta x" instead of "h" in the definition, but they are equivalent.
- Students often struggle with understanding what f(x + h) and f(x) represent in the definition.
Examples of Finding fx + h
- Given a function f(x), to find fx + h, replace x with (x + h).
- A simple method is to copy the function and replace x with (x + h).
Factorizing in Derivatives
- Factorizing is a common technique used in derivatives.
- To factorize, ensure that each term has an "h" before factorizing it.
Factorizing in Derivatives
This section focuses on factorizing expressions involving "h" in derivatives.
Factorizing "h"
- To factorize "h," ensure that each term has an "h" before factorizing it.
- Divide each term by "h" to eliminate one instance of "h."
Example 1: Factorizing with "h"
- Divide each term by "h" to eliminate one instance of "h."
- Resulting factors will be simplified expressions without any instances of "h."
Example 2: Factorizing with Multiple Instances of "h"
- Divide each term by the common factor, which is "h."
- Eliminate one instance of "h" from each term.
Practice Exercises
This section provides practice exercises for applying the concepts of finding fx + h and factorizing expressions involving "h" in derivatives.
Exercise 1: Finding fx + h
- Given a function f(x), find fx + h by replacing x with (x + h).
- Simplify the expression to obtain the result.
Exercise 2: Factorizing with "h"
- Factorize each expression by ensuring that each term has an "h" before factorizing it.
- Divide each term by "h" to eliminate one instance of "h."
Conclusion
In this video, we learned about the definition of derivatives, how to find fx + h, and how to factorize expressions involving "h" in derivatives. Practice exercises were provided to reinforce these concepts.