how to evaluate divergence of a function

**HallsofIvy** · November 23rd 2011, 04:38 AM

First, this isn't a "differential equation" nor are you asked to "evaluate" anything. You are asked to find gradient of the function $f(x,y,z)= \frac{1}{x^2+ y^2+ z^2}= (x^2+ y^2+ z^2)^{-1}$

The derivatives are fairly straight forward. By the chain rule,
$\frac{\partial f}{\partial x}= -1(x^2+ y^2+ z^2)^{-2}\frac{\partial (x^2+ y^2+ z^2)}{\partial x}= \frac{-2x}{(x^2+ y^2+ z^2)^2}$

Can you do the other two partial derivatives?

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how to evaluate divergence of a function

Re: how to evaluate this simple partial differential equation.

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