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...

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...

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

notation in a given context. For more specialized settings—such as partial derivatives in multivariable calculus, tensor analysis, or vector calculus—other...

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...

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...

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...

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

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

function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals...

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

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...

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

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

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...

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...

mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function...

quantities (known in calculus as partial derivatives; first-order or higher) representing the sensitivity of the price of a derivative instrument such as an option...

the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued...

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

formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely...

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...

the gauge covariant derivative D μ {\displaystyle D_{\mu }} as a generalisation of the partial derivative ∂ μ {\displaystyle \partial _{\mu }} that acts...

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...

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 derivative of the velocity is the acceleration d v d t = a ( t ) . {\displaystyle {\frac {d\mathbf {v} }{dt}}=\mathbf {a} (t).} The partial derivative...

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

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...