Multivariable and Vector Calculus by Sarhan M. Musa & David A. Santos

Author:Sarhan M. Musa & David A. Santos [Sarhan M. Musa]
Language: eng
Format: epub, mobi
Publisher: Mercury Learning and InformMation
Published: 2014-02-09T05:00:00+00:00

Example 2.5.6

* * *

Let f (u, v, w) = euv cos w. Determine at

Solution:

We have

which is at the desired point.

Example 2.5.7

* * *

The equation zxy + (xy)z + xy2z3 = 3 defines z as an implicit function of x and y. Find

Solution:

We have

Hence, at (1, 1, 1), we have

Similarly,

Hence, at (1, 1, 1), we have

Just like in the one-variable case, we have the following rules of differentiation. Let be open sets be differentiable on A, and be differentiable on B, and Then we have

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