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The 38 pages that link to Partial derivative, each with the reason it gives.

• DerivativeBroader topic: It adapts the ordinary derivative to functions with several independent variables.

• Partial differential equationBroader topic: PDEs are built from derivatives taken with respect to selected variables.

• GradientRelated: The gradient collects the partial derivatives with respect to each coordinate.

• Jacobian matrixBroader topic: Each Jacobian entry is a partial derivative of one output with respect to one input.

• DivergenceNarrower topic: Each coordinate term in divergence is a partial derivative of one field component.

• DifferentiabilityBroader topic: Partial derivatives are directional slices of change, but their existence alone need not ensure differentiability.

• Directional derivativeBroader topic: It is the directional derivative along a coordinate axis.

• Euler–Lagrange EquationRelated: The equation differentiates the integrand with respect to the function and its derivative separately.

• Hessian matrixNarrower topic: Partial derivatives are the operations applied twice to form Hessian entries.

• LaplacianNarrower topic: The Euclidean Laplacian sums second partial derivatives along coordinate directions.

• Divergence theoremRelated: Divergence is built from partial derivatives of the field’s components.

• Material derivativeCompared with: It captures only fixed-position change, not transport through spatial variation.

• Implicit function theoremRelated: The theorem’s Jacobian is assembled from partial derivatives.

• Green's theoremRelated: Green's theorem integrates combinations of partial derivatives across the region.

• CurlRelated: Curl is assembled from spatial partial derivatives of field components.

• Stokes' theoremRelated: Curl is built from partial derivatives of the field's components.

• Cauchy–Riemann equationsRelated: Each equation matches derivatives taken along the real and imaginary coordinate directions.

• Error propagationRelated: Each partial derivative weights one input’s contribution to output uncertainty.

• Vector calculusRelated: Partial derivatives combine into the gradient, divergence, and curl.

• Exterior derivativeCompared with: Coordinate formulas for the exterior derivative use partial derivatives but combine them independently of coordinates.

• Total derivativeCompared with: It excludes mediated changes that the total derivative includes.

• Fréchet derivativeCompared with: Coordinatewise derivatives alone need not provide a linear approximation with negligible error.

• Tensor calculusCompared with: Unlike a covariant derivative, it does not generally transform as a tensor when applied to tensor components.

• Ceteris paribusRelated: It formalizes a ceteris paribus change for functions of several variables.

• Complex derivativeRelated: Real and imaginary partial derivatives provide the components tested by the Cauchy–Riemann equations.

• Implicit differentiationCompared with: Unlike partial differentiation, the method treats linked variables as dependent along a curve.

• Leibniz notationBroader topic: The partial-derivative symbol adapts Leibniz's differential form to multiple variables.

• Implicit functionRelated: Partial derivatives appear in the conditions and formulas for implicit differentiation.

• Multivariable calculusBroader topic: It isolates change along one coordinate direction.

• Gibbs–Helmholtz equationBroader topic: The fixed-pressure temperature derivative is essential to the equation’s meaning.

• Leibniz integral ruleRelated: The integrand’s parameter dependence is differentiated while its integration variable is held fixed.

• Time derivativeCompared with: It distinguishes change with time alone from change when other inputs vary too.

• Rademacher's theoremCompared with: Existence of coordinatewise derivatives alone is weaker than the theorem’s full linear approximation.

• Function of several real variablesBroader topic: It isolates the function's local change along each coordinate direction.

• Hellmann–Feynman theoremRelated: It isolates the energy’s response to one chosen Hamiltonian parameter.

• Internal pressureRelated: The constant-temperature constraint is essential to interpreting the defining derivative.

• Jacobian matrix and determinantBroader topic: Each Jacobian entry differentiates one output component with respect to one input coordinate.

• Symmetry of second derivativesNarrower topic: Mixed derivatives are built by applying partial differentiation successively.