The chain rule is a formula used in calculus to find the derivative of a composite function. It expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. The rule is sometimes abbreviated as (f ∘ g) = f'(g)g'. In simpler terms, the chain rule tells us how to differentiate composite functions.
The rule can be applied to composites of more than two functions. To take the derivative of a composite of more than two functions, notice that the composite of f, g, and h (in that order) is the composite of f with g ∘ h. The chain rule states that to compute the derivative of f ∘ g ∘ h, it is sufficient to compute the derivative of f and the derivative of g ∘ h. The derivative of f can be calculated directly, and the derivative of g ∘ h can be calculated by applying the chain rule again.
The chain rule is one of the important rules in differentiation. It is used any time you take the derivative. The rule is helpful when differentiating composite functions that means a function of a function. In general, the chain rule is used to identify the “inside function” and the “outside function”. We then differentiate the outside function leaving the inside function alone and multiply it by the derivative of the inside function.
