This rule is called the chain rule because we use it to take derivatives of composties of functions by chaining together their derivatives. The chain rule can be thought of as taking the derivative of the outer function (applied to the inner function) and multiplying it times the derivative of the inner function.

Why is chain rule useful?

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. It tells us how to differentiate composite functions.

How does chain rule work?

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 constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².