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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 constructed as f(g(x)) for f(x)=sin(x) and g(x)=x². Using the chain rule and the derivatives of sin(x) and x², we can then find the derivative of sin(x²).

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The big idea of differential calculus is the concept of the derivative, which essentially gives us the direction, or rate of change, of a function at any of its points. Learn all about derivatives and how to find them here.

Part 4 of derivatives. Introduction to the chain rule.

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.

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

Practice applying the chain rule.

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

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.