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Gradient Determination of Functions

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Calculate the gradient Vf of the following functions, f(x,y,z)
a. f = x^2 + z^3
b. f = ky where k is a constant
c. f = r = (x^2 + y^2 + z^2)^1/2 Hint use the chain rule
d. f = 1/r

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The Del operator is a vector operator. This means that it has three components (in three dimensional space) and it operates on a scalar function:

When applied to a scalar function this ...

Solution Summary

This solution contains step-by-step calculations to determine the gradient of the vector operator using cross product and chain rule.

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How do they come up with the equations in (308) mathematically? Why do (308) give solutions to (285) and (286). Or why do (308) determine whether (285) and (286) have 1 or more solutions? I don't wonder about the proof for why the La place (309) introduced as a general equation later in the text has only 1 solution. Thanks

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