In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions z and y in terms of the derivatives of z and y.

The chain rule formula states that dy/dx = dy/du × du/dx. In words, differentiate the outer function while keeping the inner function the same then multiply this by the derivative of the inner function.

Apr 23, 2026 · In this section we discuss one of the more useful and important differentiation formulas, The Chain Rule. With the chain rule in hand we will be able to differentiate a much wider variety of …

There are rules we can follow to find many derivatives. For example: and so on. If we know the rate of change for two related things, how do we work out the overall rate of change? The Chain Rule tells …

Nov 1, 2025 · It is one of the basic rules used in mathematics for solving differential equations. It helps us to find the derivative of composite functions such as (3x2 + 1)4, (sin 4x), e3x, (ln x)2, and others. …

Nov 18, 2025 · Master the chain rule in calculus with our comprehensive guide. Learn how to find derivatives of composite functions with clear explanations, step-by-step examples, practice …

Instead, we use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.

The chain rule formula is mainly used to find the derivative of a composite function (a function that is the combination of two or more functions). This chain rule has broad applications in physics, chemistry, …

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. Brush up on your knowledge of composite functions, and learn how to apply the chain rule correctly.