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...

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...

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...

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...

{\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...