Formula for the Derivative of the Absolute Value of Any Function
TL;DR
This video explains how to find the derivative of the absolute value of any function by using a formula, and also demonstrates how to find the derivative without the formula.
Transcript
okay YouTube in this video I'm going to show you how to come up with the formula for the derivative of the absolute value of any function as long as you can take the derivative of the function and then we're gonna use the formula to find the derivative and then we'll do it without the formula as well so let's start by finding the derivative of the ... Read More
Key Insights
- ❎ The derivative of the absolute value of a function can be found by replacing the absolute value with the square root of the function squared.
- 📏 The chain rule is used to find the derivative, with the derivative of the inside function multiplied by the derivative of the absolute value.
- ❓ The formula for the derivative of the absolute value of a function is f'(x) * f(x) / |f(x)|.
- ❎ The process for finding the derivative without the formula involves replacing the absolute value with the square root of the function squared and using the chain rule.
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Questions & Answers
Q: What is the formula to find the derivative of the absolute value of a function?
The formula is f'(x) * f(x) / |f(x)|, where f'(x) is the derivative of the function and f(x) is the function itself.
Q: When can the chain rule be used to find the derivative of the absolute value of a function?
The chain rule can be used to find the derivative when the derivative of the function is not zero and when it is defined everywhere.
Q: What is the process for finding the derivative of the absolute value of a function without using the formula?
The process involves replacing the absolute value with the square root of the function squared, and then using the chain rule to find the derivative.
Q: Why is it useful to write the absolute value as the square root of the function squared?
Writing the absolute value this way allows us to simplify the expression and make it easier to find the derivative.
Summary & Key Takeaways
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The video explains the process of finding the derivative of the absolute value of a function by replacing the absolute value with the square root of the function squared.
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The chain rule is used to find the derivative, with the derivative of the inside function being multiplied by the derivative of the absolute value.
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The formula for the derivative of the absolute value of a function is given as f'(x) * f(x) / |f(x)|.
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