Linked from

The 24 pages that link to Directional derivative, each with the reason it gives.

• DerivativeBroader topic: It generalizes the one-dimensional rate to change along chosen directions.

• GradientRelated: The gradient’s dot product with a direction vector gives this rate of change.

• Partial derivativeCompared with: A general direction can combine coordinate changes instead of varying one coordinate alone.

• Lagrange multiplierRelated: Constrained optimality concerns changes along directions allowed by the constraint.

• Tangent spaceRelated: Tangent vectors can be defined by how they differentiate smooth functions.

• Scalar fieldRelated: It measures how the field changes along a specified direction.

• DivergenceCompared with: It measures change along one direction, not net flow across all directions.

• Covariant derivativeRelated: Covariant differentiation generalizes directional differentiation from scalar functions to geometric fields.

• Gradient descentRelated: The negative gradient selects a direction of local decrease.

• DifferentiabilityRelated: Existence in every direction is weaker than full differentiability in several variables.

• LaplacianCompared with: Unlike a single directional rate, the Laplacian combines second-order change across directions.

• Affine connectionCompared with: Unlike ordinary directional differentiation, a connection compares tangent vectors at different manifold points.

• Complex differentiabilityCompared with: Existence in individual directions does not ensure one direction-independent complex difference-quotient limit.

• Vector calculusRelated: The gradient gives every directional derivative through a dot product.

• Total derivativeRelated: A total derivative along a parameterized path is a directional rate of change.

• Fréchet derivativeCompared with: Directional derivatives can exist in every direction without forming a Fréchet derivative.

• Complex derivativeCompared with: A complex derivative must agree with the difference-quotient limit along every direction.

• Unit sphereRelated: Directions of unit length are points on the unit sphere, making comparisons independent of scale.

• Differentiable functionCompared with: Existence in every direction does not by itself guarantee a linear derivative.

• Multivariable calculusBroader topic: It extends partial derivatives beyond coordinate directions.

• Second derivativeCompared with: A directional derivative is first-order change, whereas the Hessian captures second-order change.

• Function of several real variablesRelated: It measures local change beyond the coordinate directions used by partial derivatives.

• Interior extremum theoremRelated: At an interior extremum, opposite directional changes force every directional derivative to vanish.

• Symmetry of second derivativesCompared with: Directional derivatives concern chosen directions, not interchange of coordinate differentiation orders.