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...

{\displaystyle {\frac {\partial f}{\partial x}}=2x+y,\qquad {\frac {\partial f}{\partial y}}=x+2y.} In general, the partial derivative of a function f ( x...

In mathematics, the second partial derivative test is a method in multivariable calculus used to determine if a critical point of a function is a local...

)}{\partial \mathbf {x} }}.} It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear...

derivative of a function f at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives...

calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a...

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...

_{a(x)}^{b(x)}{\frac {\partial }{\partial x}}f(x,t)\,dt\end{aligned}}} where the partial derivative ∂ ∂ x {\displaystyle {\tfrac {\partial }{\partial x}}} indicates...

{\frac {\partial L}{\partial f'}}(a)\delta f(a)\end{aligned}}} where the variation in the derivative, δf ′ was rewritten as the derivative of the variation...

function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the...

the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing...

{\partial ^{2}f}{\partial x\,\partial y}},\\[5pt]&\partial _{yy}f={\frac {\partial ^{2}f}{\partial y^{2}}}.\end{aligned}}} See § Partial derivatives. D-notation...

symmetry of second derivatives (also called the equality of mixed partials) is the fact that exchanging the order of partial derivatives of a multivariate...

{\partial (u_{1},\ldots ,u_{m})}{\partial (x_{1},\ldots ,x_{n})}}.} The chain rule for total derivatives implies a chain rule for partial derivatives....

the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described...

the time derivative becomes equal to the partial time derivative, which agrees with the definition of a partial derivative: a derivative taken with...

Civita connection), then the partial derivative ∂ a {\displaystyle \partial _{a}} can be replaced with the covariant derivative which means replacing ∂ a...

usually to denote a partial derivative such as ∂ z / ∂ x {\displaystyle {\partial z}/{\partial x}} (read as "the partial derivative of z with respect to...

computational differentiation, is a set of techniques to evaluate the partial derivative of a function specified by a computer program. Automatic differentiation...

which partial derivatives exist in every direction but fail to be differentiable. Furthermore, this definition as the vector of partial derivatives is only...

Look up partial in Wiktionary, the free dictionary. Partial may refer to: Partial derivative, derivative with respect to one of several variables of a...

the mapping ƒ at point x. Each entry of this matrix represents a partial derivative, specifying the rate of change of one range coordinate with respect...

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...

Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated...

one knows the derivative for all prime numbers, then the derivative is fully known. In fact, the family of arithmetic partial derivative ∂ ∂ p {\textstyle...

(less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local...

a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Unless otherwise stated, all functions are...

curl in terms of partial derivatives. A matrix of partial derivatives, the Jacobian matrix, may be used to represent the derivative of a function between...

exterior derivative dj is then given by d j = ( ∂ F 1 ∂ x + ∂ F 2 ∂ y + ∂ F 3 ∂ z ) d x ∧ d y ∧ d z = ( ∇ ⋅ F ) ρ {\displaystyle dj=\left({\frac {\partial F_{1}}{\partial...

defined as a vector operator whose components are the corresponding partial derivative operators. As a vector operator, it can act on scalar and vector fields...