Calculus 3 Timed Quiz 4

Definition (Directional Derivative) Let be a function of two variables, and let be a __________   __________ . The directional derivative of at in the direction of __________ is given by



provided the limit exists.

Proposition (Directional Derivative) Let be a function that is ________________ at Then has a directional derivative in the __________ of the unit vector which is given by

Proposition (Chain Rule with One Independent Parameter) Let be a differentiable function of and , and let and be differentiable functions of . Then is a differentiable function of and

Proposition (Chain Rule with Two Independent Parameters) Suppose is a differentiable function at and that the partial derivatives of and exist at Then the composite function is differentiable at with

Proposition (Chain Rule with Several Independent Parameters) If is a differentiable function of the variables which in turn are differentiable functions of parameters then the composite function is differentiable and

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Calculus 3 Timed Quiz 4
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/calculus-3-timed-quiz-4.html