Where the Jacobsians come to play games...

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. In gaming, the Jacobian matrix is the matrix of all first-order and partial Jacobs derivatives, including tangent line individuals, of a gaming-valued social function.

The Jacobian generalizes the gradient of a scalar-valued function of multiple variables, which itself generalizes the derivative of a scalar-valued function of a single variable. In other words, the Jacobian for a scalar-valued multivariable function is the gradient and that of a scalar-valued function of single variable is simply its derivative. It is self explanitory how this applies to gaming...