The chain rule tells us how to find the derivative of a composite function. Brush up on your knowledge of composite functions, and learn how to apply the chain rule correctly.

The chain rule states that the derivative of f (g (x)) is f' (g (x))⋅g' (x). In other words, it helps us differentiate *composite functions*. For example, sin (x²) is a composite function because it …

Let's dive into the process of differentiating a composite function, specifically f (x)=sqrt (3x^2-x), using the chain rule. By breaking down the function into its components, sqrt (x) and 3x^2-x, …

The chain rule tells us how to find the derivative of a composite function. This is an exceptionally useful rule, as it opens up a whole world of functions (and equations!) we can now differentiate.

We'll dissect the process of finding the derivative of a function like sin (x^2)^3, demonstrating the power and adaptability of the chain rule when used not just once, but twice!

Can you evaluate h (x) = f (g (x)) and find its (that's h (x)) derivative? For example, let's say f (x) = x^2 and g (x) = x+1. Then h (x) is (x+1)^2. Expanding it will result in x^2 + 2x + 1. If you find …

Chain rule with tables AP.CALC: FUN‑3 (EU), FUN‑3.C (LO), FUN‑3.C.1 (EK) Google Classroom Microsoft Teams

Proving the chain rule for derivatives. The chain rule tells us how to find the derivative of a composite function:

Let's explore multiple strategies to tackle derivatives involving both the product and chain rules. We start by applying the chain rule first, then the product rule.

Chain rule Learn Chain rule Worked example: Derivative of cos³ (x) using the chain rule