Chain rule | Derivative rules | AP Calculus AB | Khan Academy

TL;DR

Learn how to use the chain rule in calculus to find the derivative of composite functions.

Transcript

• [Instructor] What we're going to go over in this video is one of the core principles in calculus, and you're going to use it any time you take the derivative, anything even reasonably complex. And it's called the chain rule. And when you're first exposed to it, it can seem a little daunting and a little bit convoluted. But as you see more and mor... Read More

Key Insights

• 👻 The chain rule is a fundamental concept in calculus that allows you to find the derivative of composite functions.
• ☠️ Understanding the chain rule is essential for solving problems involving rates of change and optimization.
• 🫡 The chain rule involves taking derivatives with respect to different variables and multiplying them together.
• 📏 The chain rule can be applied to functions that are composed of more than two functions.
• 🍽️ When applying the chain rule, it is important to differentiate the outer and inner functions separately and then multiply their derivatives.
• 🆘 Treating the differentials as fractions can help with intuition, but it is not mathematically rigorous.
• 📏 The chain rule can seem daunting at first, but with practice and examples, it becomes more intuitive.

Questions & Answers

Q: What is the chain rule in calculus?

The chain rule is a rule used when finding the derivative of composite functions. It allows you to find the derivative of a function composed of multiple functions.

Q: Why is the chain rule important in calculus?

The chain rule is important because it allows us to find the rate of change of complex functions. By breaking down a composite function into its individual components, we can determine how each component affects the overall function.

Q: How is the chain rule applied?

The chain rule is applied by taking the derivative of the outer function with respect to the inner function, and multiplying it by the derivative of the inner function with respect to the variable.

Q: Can the chain rule be used for any composite function?

Yes, the chain rule can be used for any composite function, as long as it can be expressed as a composition of multiple functions.

Summary & Key Takeaways

• The chain rule is a core principle in calculus used when taking the derivative of composite functions.

• The chain rule allows you to find the derivative of a function that is composed of multiple functions.

• By applying the chain rule, you can find the derivative of a composite function by multiplying the derivative of the outer function by the derivative of the inner function.