MathLiveChain rule
Gives the derivative of a composition of two functions as the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. It is used whenever a function is nested inside another, such as differentiating sin(x^2).
(f \circ g)'(x) = f'(g(x)) \cdot g'(x)What the symbols mean
| outer differentiable function | |
| inner differentiable function | |
| composition of f with g, i.e. the function x \mapsto f(g(x)) | |
| point at which the derivative is evaluated | |
| derivative of f evaluated at g(x) | |
| derivative of g at x |
About this formula
- FieldMathematics
- TopicDifferential calculus
- LevelHigh school
- Also calledderivative of composite function, differentiating composed functions, chain rule derivative, derivative of f(g(x)), composite function derivative, chain rule formula
- SourceWikidata Q207455
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