Derivatives of vector functions.

Description
Given x , a point on the n dimensional vector space and f(x) is a scalar function of x, then the derivative of f is defined and is represented by a row matrix. The notation of derivative of a vector function is expressed mathematically. Vector function of a vector variable is defined. The conditions that a function with k real valued function of n variables is diferentiable at at point, are stated and some important theorems on this are discussed. Differentiation of inverse functions are discussed. The implicit differentiation is defined.
Prof. James McKernan, Maths, 18.024. Calculus with Theory II, Spring 2003: Derivatives of vector functions: Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed October 21, 2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc