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Chain Rule

Definition

The chain rule is a formula used to find the derivative of a composition of two or more functions. It states that the derivative of a composite function is equal to the derivative of the outermost function times the derivative of the innermost function.

Analogy

Think of driving through multiple traffic lights on your way home. Each traffic light has its own timing and rules, but they all work together to get you safely home. Similarly, when you have multiple functions nested inside each other, the chain rule helps you navigate through each layer and calculate their combined effect on finding their derivatives.

Related terms

Product Rule: The product rule allows us to find derivatives when two functions are multiplied together. It helps us determine how changes in one function affect changes in another.

Quotient Rule: The quotient rule is used to find the derivative of a quotient or division between two functions. It helps us determine how changes in one function affect changes in another.

Derivative: A derivative measures how a quantity changes as its input (usually time or position) changes. In calculus, it represents instantaneous rates of change and slopes of curves at specific points.