the directional derivative measures the rate at which a function changes in a particular direction at a given point.[citation needed] The directional derivative...

directional derivatives. Given a vector ⁠ v = ( v 1 , … , v n ) {\displaystyle \mathbf {v} =(v_{1},\ldots ,v_{n})} ⁠, then the directional derivative...

{\displaystyle F} be a multivector-valued function of a vector. The directional derivative of F {\displaystyle F} along b {\displaystyle b} at a {\displaystyle...

is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known...

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held...

Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean directional derivative onto the manifold's tangent...

monograph provides a formula for the directional derivative of the maximum of a (not necessarily convex) directionally differentiable function. An extension...

expressions for the gradient, divergence, curl, directional derivative, and Laplacian. The vector derivative of a scalar field f {\displaystyle f} is called...

difference in the definition of the limit and differentiation. Directional limits and derivatives define the limit and differential along a 1D parametrized...

covariant derivative makes a choice for taking directional derivatives of vector fields along curves. This extends the directional derivative of scalar...

logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle {\frac {f'}{f}}} where f ′ {\displaystyle f'} is the derivative of f....

derivative of the field u·(∇y), or as involving the streamline directional derivative of the field (u·∇) y, leading to the same result. Only this spatial...

simulations. The directional derivative provides a systematic way of finding these derivatives. The definitions of directional derivatives for various situations...

as directional derivatives. Given a vector v {\displaystyle v} in R n {\displaystyle \mathbb {R} ^{n}} , one defines the corresponding directional derivative...

derivative of a function on a differentiable manifold, the most fundamental of which is the directional derivative. The definition of the directional...

of the total derivative Gateaux derivative – Generalization of the concept of directional derivative Generalizations of the derivative – Fundamental...

Fréchet derivative should be contrasted to the more general Gateaux derivative which is a generalization of the classical directional derivative. The Fréchet...

every smooth vector field X, df (X) = dX f , where dX f  is the directional derivative of  f  in the direction of X. The exterior product of differential...

applications, the directional derivative is indeed sufficient. The above arithmetic can be generalized to calculate second order and higher derivatives of multivariate...

Rn or in a Banach space. Directional derivative Partial derivative Gradient Gateaux derivative Fréchet derivative Derivative (generalizations) Phase space...

typically given in the form of a covariant derivative, which gives a means for taking directional derivatives of vector fields, measuring the deviation...

a branch of mathematics, the third derivative or third-order derivative is the rate at which the second derivative, or the rate of change of the rate...

mathematics, the Gateaux differential or Gateaux derivative is a generalization of the concept of directional derivative in differential calculus. Named after René...

derivative of a tensor field with respect to a vector field would be to take the components of the tensor field and take the directional derivative of...

derivative, a generalization of the concept of directional derivative in differential calculus. Lie derivative, the change of a tensor field (including scalar...

notation just defined for the derivative of a scalar with respect to a vector we can re-write the directional derivative as ∇ u f = ∂ f ∂ x u . {\displaystyle...

second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative can be...

path-independent. Let v be any nonzero vector in Rn. By the definition of the directional derivative, ∂ f ( x ) ∂ v = lim t → 0 f ( x + t v ) − f ( x ) t = lim t → 0...

strength, usually a first-order derivative expression such as the gradient magnitude, and then searching for local directional maxima of the gradient magnitude...

of the proof is to show that, for any fixed unit vector v, the v-directional derivative of u exists almost everywhere. This is a consequence of a special...