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

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

• 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.

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

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

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

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

• 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.

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

• 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.

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

• 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.

• 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.

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

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

• Logistic functionRelated: The logistic function’s derivative is proportional to the function times one minus itself.

• Secant methodRelated: The secant method estimates this quantity from function values rather than evaluating it.

• Bernoulli's inequalityRelated: The derivative at zero determines the slope of the linear expression in the bound.

• Hyperreal numberRelated: A derivative can be expressed as the standard part of a hyperreal difference quotient.

• One-sided limitRelated: At domain boundaries, a derivative may be defined using only one approach direction.

• Real-valued functionRelated: For real-valued functions, derivatives quantify local output change when the domain supports differentiation.

• Constant functionRelated: Every differentiable constant function has derivative zero throughout its domain.

• Differentiable functionRelated: It is the linear map that defines differentiability at a point.

• Parametric equationRelated: Coordinate derivatives reveal the direction and speed of a parameterized curve.

• Guillaume de l’HôpitalRelated: Derivatives are the central objects developed in l’Hôpital’s calculus text.

• Brook TaylorRelated: Successive derivatives supply the coefficients in Taylor’s expansion.

• Cubic functionRelated: The derivative of a cubic is quadratic and locates its stationary points.

• Metre per second squaredRelated: Acceleration is the time derivative of velocity.

• Stolz–Cesàro theoremRelated: The theorem is a discrete analogue of comparing derivatives to evaluate quotient limits.

• Function of a real variableRelated: It measures local change in the output as the real input varies.

• Standard part functionRelated: An infinitesimal difference quotient yields the derivative after taking its standard part.