Derivadas Regla de la cadena | Función compuesta | Ejemplo 1

Introduction

In this section, the speaker introduces the topic of finding the derivative of a composite function or using the chain rule. They mention that this is the first video in which they will cover the chain rule and provide an overview of what will be covered in future videos.

Derivative of a Composite Function

• The speaker mentions that they will start with an easy example to introduce the concept.

• They explain that the chain rule is used when there is a parenthesis with an operation outside, such as an exponent, sine, logarithm, or exponential.

• The speaker simplifies the chain rule by explaining that it involves taking two derivatives: one for what's inside the parenthesis and one for what's outside.

• They demonstrate how to apply the chain rule by taking derivatives step by step.

• The speaker emphasizes that when taking the derivative of what's outside, nothing changes inside. Only the exponent is lowered and subtracted by 1.

• They also show how to take the derivative of what's inside separately without considering the exponent.

Example 1

In this section, an example is provided to illustrate how to apply the chain rule.

Applying Chain Rule to Example 1

• The speaker applies the chain rule to find the derivative of a given function.

• They lower and subtract 1 from the exponent outside while keeping everything inside unchanged.

• Then they take only the derivative of what's inside separately.

• Finally, they multiply both derivatives together and simplify.

Example 2

In this section, another example is presented to further demonstrate how to use the chain rule.

Applying Chain Rule to Example 2

• The speaker applies similar steps as in Example 1 to find the derivative of a different function.

• They lower and subtract 1 from the exponent outside while keeping everything inside unchanged.

• Then they take only the derivative of what's inside separately.

• Finally, they multiply both derivatives together and simplify.

Conclusion

In this section, the speaker concludes the lesson and encourages viewers to practice applying the chain rule on their own. They provide two additional exercises for practice.

Practice Exercises

• The speaker presents two exercises for viewers to solve using the chain rule.

• They demonstrate how to apply the chain rule step by step in each exercise.

• The solutions are provided after a brief pause for viewers to attempt solving them on their own.

Timestamps may not be exact due to differences in transcription and video playback.