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Physics / Classical Mechanics 0 / Chapter 4 / Problem 4.13

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

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Solved: Calculate the gradient Vf of the following

Chapter 4, Problem 4.13

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QUESTION:

Calculate the gradient Vf of the following functions, f (x, y, z): (a) f = ln(r ), (b) f = rn, (c) f = g(r), where r = ,./x2 + y2 + z2 and g(r) is some unspecified function of r. [Hint: Use the chain rule.]

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QUESTION:

Calculate the gradient Vf of the following functions, f (x, y, z): (a) f = ln(r ), (b) f = rn, (c) f = g(r), where r = ,./x2 + y2 + z2 and g(r) is some unspecified function of r. [Hint: Use the chain rule.]

ANSWER:

Step 1 of 4

(a)

The term gradient refers to a vector field that can be obtained by applying a vector operator to a scalar function. The gradient of a function represents the greatest/maximum change in the direction.

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