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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 can apply to composing multiple functions, not just two. For example, suppose A (x) , B (x) , C (x) and D (x) are four different functions, and define f to be their composition:

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!

Saul has introduced the multivariable chain rule by finding the derivative of a simple multivariable function by applying the single variable chain and product rules.

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

If we write f of x being equal to v of u of x, then we see very clearly the chain rule is very useful here. The chain rule tells us that f prime of x is going to be the derivative of v, with respect to u.

Unit 3: Derivatives: chain rule and other advanced topics 1,600 possible mastery points Mastered Proficient

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