If is Differentiable at the point and is Differentiable at the point , then
is Differentiable at . Furthermore, let and , then

(1) |

(2) |

(3) | |||

and

(4) | |||

Defining the Jacobi Matrix by

(5) |

(6) |

(7) |

**References**

Anton, H. *Calculus with Analytic Geometry, 2nd ed.* New York: Wiley, p. 165, 1984.

Kaplan, W. ``Derivatives and Differentials of Composite Functions'' and ``The General Chain Rule.'' §2.8 and 2.9 in
*Advanced Calculus, 3rd ed.* Reading, MA: Addison-Wesley, pp. 101-105 and 106-110, 1984.

© 1996-9

1999-05-26