iSoul In the beginning is reality.

# Vectors and functions

Vectors and functions is here in pdf form.

The quotient of an n-dimensional vector variable or vector-valued function x with a scalar variable t equals

The quotient of a scalar variable x with an n-dimensional vector variable or vector-valued function t equals

The quotient of an n-dimensional vector variable or vector-valued function x with an independent n-dimensional vector variable or vector-valued function t equals

The derivative of an n-dimensional vector function x with respect to an independent scalar variable t equals

The directional derivative of a scalar function x with respect to an independent n-dimensional vector variable t equals

The directional derivative of an n-dimensional vector-valued function x with respect to an n-dimensional vector variable t equals

The matrix is a square Jacobian matrix, whose (i, j)th entry is

The inverse function theorem states that the matrix inverse of the Jacobian matrix of an invertible function is the Jacobian matrix of the inverse function.