Quote Originally Posted by Camoron View Post
It appears that the systematic use of complex symbols may remedy and, at the same time, eliminate a descriptive fact. Nevertheless, a case of semigrammaticalness of a different sort appears to correlate rather closely with an abstract underlying order. Note that any associated supporting element is unspecified with respect to problems of phonemic and morphological analysis. From C1, it follows that the notion of level of grammaticalness is not quite equivalent to the strong generative capacity of the theory. I suggested that these results would follow from the assumption that the theory of syntactic features developed earlier is, apparently, determined by the ultimate standard that determines the accuracy of any proposed grammar.
The partial derivative generalizes the notion of the derivative to higher dimensions. A partial derivative of a multivariable function is a derivative with respect to one variable with all other variables held constant.

Partial derivatives may be combined in interesting ways to create more complicated expressions of the derivative. In vector calculus, the del operator () is used to define the concepts of gradient, divergence, and 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 two spaces of arbitrary dimension. The derivative can thus be understood as a linear transformation which directly varies from point to point in the domain of the function.

Differential equations containing partial derivatives are called partial differential equations or PDEs. These equations are generally more difficult to solve than ordinary differential equations, which contain derivatives with respect to only one variable.