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...

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...

{\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...

)}{\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...

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...

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

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...

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...

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