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 …

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!

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, …

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.

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.

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

Use the chain rule to differentiate composite functions like sin (2x+1) or [cos (x)]³.

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.

Well we just said u is equal to sine of x, you reverse substitute, and you're going to get exactly that right over here. So when we talk about the reverse chain rule, it's essentially just doing u …