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The 80 pages that link to Derivative, each with the reason it gives.

• Differential equationNarrower topic: Differential equations use derivatives to encode rates of change.

• Taylor seriesNarrower topic: Each Taylor coefficient uses a derivative evaluated at the expansion point.

• Ordinary differential equationNarrower topic: Derivatives of the unknown function are the quantities an ODE relates.

• Newton's methodNarrower topic: The derivative supplies the tangent slope used to calculate each update.

• Chain ruleNarrower topic: The chain rule combines derivatives to obtain the rate of change of a composition.

• SlopeNarrower topic: For a curve, the derivative gives the slope of its tangent at a point.

• Fundamental theorem of calculusNarrower topic: The theorem connects this local rate to integral accumulation.

• Taylor's theoremNarrower topic: Taylor coefficients use successive derivatives to encode local behavior.

• Inverse function theoremNarrower topic: The theorem uses this local linear approximation to establish nonlinear invertibility.

• Legendre transformNarrower topic: The transformed variable is the derivative with respect to the variable being replaced.

• Marginal analysisNarrower topic: In continuous models, derivatives express the rates used to compare marginal quantities.

• Mean value theoremNarrower topic: The theorem guarantees that this local rate matches a specified interval-wide rate.

• Taylor polynomialNarrower topic: Repeated derivatives supply the local data used in each coefficient.

• Implicit differentiationNarrower topic: Implicit differentiation’s goal is to determine a derivative from a relation.

• Second derivative testNarrower topic: The test uses the second derivative, which measures how the first derivative changes.

• Indeterminate formNarrower topic: L'Hôpital's rule turns certain indeterminate limits into limits involving derivatives.

• L'Hôpital's ruleNarrower topic: The rule replaces a quotient of functions with a quotient of their derivatives.

• Related ratesNarrower topic: Each unknown rate in a related-rates problem is a derivative.

• Leibniz notationNarrower topic: The derivative is the operation represented by dy/dx.

• Constant of integrationNarrower topic: The derivative is the operation that cannot detect an added constant.

• Logarithmic differentiationNarrower topic: Logarithmic differentiation is a technique for finding this quantity.

• Second derivativeNarrower topic: The second derivative is obtained by differentiating this function again.

• Cauchy's mean value theoremNarrower topic: The theorem links a ratio of derivatives to a ratio of finite differences.

• Time derivativeNarrower topic: A time derivative is the derivative whose input is time.

• Instantaneous velocityNarrower topic: Instantaneous velocity is the derivative of position with respect to time.

• Denjoy–Luzin theoremNarrower topic: The theorem applies to derivatives, whether or not those derivatives are continuous.

• Differentiation of trigonometric functionsNarrower topic: Trigonometric differentiation is a collection of derivative rules for specific functions.

• Differentiation rulesNarrower topic: Every differentiation rule computes this quantity from a function’s structure.

• Interior extremum theoremNarrower topic: The theorem’s one-dimensional conclusion is stated in terms of this quantity.