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...

)}{\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...

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...

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...

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

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...

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...

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