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 …

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.

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 …

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 …

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 …

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.

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

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.