If is Differentiable at the point and is Differentiable at the point , then
is Differentiable at . Furthermore, let and , then
(1) |
(2) |
(3) | |||
(4) | |||
(5) |
(6) |
(7) |
See also Derivative, Jacobian, Power Rule, Product Rule
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 Eric W. Weisstein