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 …

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.

Chain rule Identifying composite functions Worked example: Derivative of cos³ (x) using the chain rule Worked example: Derivative of √ (3x²-x) using the chain rule Worked example: Derivative …

The Fundamental Theorem of Calculus tells us how to find the derivative of the integral from 𝘢 to 𝘹 of a certain function. But what if instead of 𝘹 we have a function of 𝘹, for example sin (𝘹)? Then 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.

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.

Understanding the derivative of f (g (t)) requires understanding how a tiny change in t changes the final output. So let's dive into what the chain rule is really saying.

Through a worked example, we explore the Chain rule with a table. Using specific x-values for functions f and g, and their derivatives, we collaboratively evaluate the derivative of a …

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