Linked from

The 34 pages that link to Chain rule, each with the reason it gives.

• DerivativeRelated: It handles derivatives when one function is nested inside another.

• GradientRelated: It explains how gradients transform when coordinates or variables change.

• Jacobian matrixRelated: Jacobians of composed functions multiply in the same order as their derivative maps.

• Partial derivativeRelated: It propagates partial derivatives through functions whose inputs depend on other variables.

• CalculusRelated: It lets derivatives track how change passes through nested dependencies.

• Function compositionRelated: It computes derivatives by tracking each function in the composition.

• Implicit function theoremRelated: Differentiating the defining equation yields the derivative formula for the implicit function.

• Differential calculusRelated: It carries rates of change through nested functions.

• Change of variablesRelated: Derivatives of transformed expressions follow by applying the chain rule.

• AntiderivativeRelated: Recognizing a reversed chain rule often reveals an antiderivative by substitution.

• Total derivativeRelated: The total derivative is the chain rule applied to every path by which the input affects the quantity.

• Fréchet derivativeRelated: For Fréchet derivatives, composition corresponds to composing the associated linear maps.

• Implicit differentiationRelated: Differentiating a term involving the dependent variable requires multiplying by that variable’s derivative.

• Related ratesRelated: It converts a changing quantity’s derivative into its rate multiplied by its dependence on another variable.

• Leibniz notationRelated: Leibniz notation displays the intermediate differentials that compose under this rule.

• Differentiable functionRelated: It combines local linear approximations by composing their derivative maps.

• Implicit functionRelated: Differentiating an implicit relation uses the chain rule to connect dependent and independent variables.

• Logarithmic differentiationRelated: Differentiating the logarithm introduces a factor of the original function's derivative.

• Multivariable calculusRelated: It tracks how changes propagate through nested multivariable functions.

• Second derivativeRelated: Repeated differentiation of composite functions often requires applying this rule at each stage.

• Leibniz integral ruleRelated: It accounts for how parameter-dependent limits change with the parameter.

• Time derivativeRelated: It converts derivatives between time and another variable when quantities depend on both.

• Vector-valued functionRelated: It combines rates of change when vector-valued functions are composed.

• Gradient theoremRelated: Applied to the scalar field along a parametrized path, it turns the integrand into a derivative along the path.

• Integrating factorRelated: Recovering a potential from an exact differential uses the chain rule in reverse.

• Differentiation of trigonometric functionsRelated: It extends basic trigonometric formulas to expressions such as sine of a function.

• Function of several real variablesRelated: It computes change when several inputs depend on other variables.

• Jacobian matrix and determinantRelated: Jacobian matrices of successive transformations multiply according to this rule.