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 can be …

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, we …

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.

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.

To do the chain rule you first take the derivative of the outside as if you would normally (disregarding the inner parts), then you add the inside back into the derivative of the outside.

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

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

We also emphasize the importance of fully applying the Chain Rule, and avoid the pitfall of taking the derivative of the outer function with respect to the derivative of the inner function.

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