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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 can be …

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 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:

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.

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.

Practice applying the chain rule. So we can give you the right tools, let us know if you're a...

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!

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

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-substitution in …