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

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

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

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

• 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.

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

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

• 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.