Solved: Gradient fields Find the gradient field F = for

Chapter 14, Problem 30E

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QUESTION:

Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the following potential functions \(\varphi\).

\(\varphi(x, y, z)=\ln \left(1+x^{2}+y^{2}+z^{2}\right)\)


Text Transcription:

varphi(x, y, z) = ln 1+x^2+y^2+z^2

Questions & Answers

QUESTION:

Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the following potential functions \(\varphi\).

\(\varphi(x, y, z)=\ln \left(1+x^{2}+y^{2}+z^{2}\right)\)


Text Transcription:

varphi(x, y, z) = ln 1+x^2+y^2+z^2

ANSWER:

Solution 30EStep 1:Given that(x,y,z) = In (1 + x2 + y2 + z2)

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