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Expansion of (a ± b ± c)²

If u=1/√x2+...

Question

If $u = \frac{1}{\sqrt{x^{2} + y^{2} + z^{2}}}$ then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} + z \frac{\partial u}{\partial z} =$

u

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- u

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2 u

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- 2 u

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Solution

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⎛ ⎜ ⎜ ⎜ ⎜ ⎝ \frac{x \frac{\partial^{2} u}{\partial x^{2}} + y \frac{\partial^{2} u}{\partial x \partial y}}{\frac{\partial u}{\partial x}} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠

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