Linked from

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.

• Exponential functionRelated: Exponential functions are proportional to their own derivatives, with a factor set by the base.

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

• AccelerationRelated: Acceleration is the time derivative of velocity.

• Sensitivity analysisRelated: Derivatives provide local measures of model-output response to parameter changes.

• VelocityRelated: Differentiating position with respect to time gives instantaneous velocity.

• Limit of a functionRelated: A derivative exists when nearby average rates approach a definite value.

• Finite differenceCompared with: A derivative is a limiting rate; a finite difference measures change across a nonzero interval.

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

• CalculusBroader topic: It formalizes instantaneous change, the central operation of differential calculus.

• Arc lengthRelated: Coordinate derivatives give the curve's instantaneous velocity.

• SineRelated: The derivative of sine is cosine, linking the functions through change.

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

• DifferentiabilityBroader topic: Differentiability at a point means this limit exists there.

• Tangent lineRelated: At a differentiable point, the derivative gives the tangent line’s slope.

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

• Line integralRelated: Differentiating a curve’s parametrization gives the tangent used in vector integrals.

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

• Marginal costRelated: It formalizes marginal cost when total cost varies smoothly with output.

• SpeedRelated: Differentiating position with respect to time gives velocity and its magnitude gives speed.

• Difference quotientBroader topic: Taking the interval length toward zero turns the quotient into a derivative.

• Secant lineBroader topic: It is the limiting slope of secant lines as one point approaches the other.

• CurvatureRelated: Differentiation quantifies the local changes used in curvature formulas.

• Differential calculusBroader topic: The derivative is differential calculus’s central quantity.

• Gaussian functionRelated: Differentiation of a Gaussian produces a linear factor times the same exponential.

• InfinitesimalRelated: In nonstandard analysis, it can be computed from an infinitesimal change in input.

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

• Monotonic functionRelated: A derivative with a consistent sign on an interval implies monotonicity there.

• 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.

• Multiplicity of a rootRelated: Vanishing successive derivatives at a root help identify its multiplicity.

• Piecewise functionRelated: Even continuous pieces may have different slopes where their formulas meet.

• AntiderivativeRelated: An antiderivative is defined by having this function as its derivative.

• Euler's NumberRelated: The natural exponential is the unique exponential function equal to its own derivative.

• Integral calculusRelated: Integration recovers functions from derivatives and accumulates changing rates.

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

• Nonstandard analysisRelated: Its value is the standard part of a hyperreal infinitesimal difference quotient.

• Weierstrass functionRelated: The function lacks this limit at every point in its domain.

• Graph of a functionRelated: The graph's tangent slope represents the derivative where it exists.

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

• Darboux's theoremCompared with: Darboux's theorem is stronger than the intermediate-value property of arbitrary functions because it applies specifically to derivatives.

• 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.

• Absolute continuityRelated: Absolutely continuous functions have integrable derivatives that recover their increments.

• Falling factorialCompared with: Unlike differentiation of powers, finite differences lower falling-factorial order without changing its basic form.

• Indefinite integralRelated: An indefinite integral reverses differentiation by seeking functions with a specified derivative.

• 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.