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The rs are unit vectors. &nbsp; &nbsp;I do not think your starting equation is<br />
grad(dg/dr) dot grad r
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The rs are unit vectors.    I do not think your starting equation is
grad(dg/dr) dot grad r

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The same equation can be derived if you assume that r is a function of (x,y,z) with r(x,y,z) = sqrt(x^2+y^2+z^2). In which case, grad r = (x,y,z)/||(x,y,z)||, which we can call r hat.<br />

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The same equation can be derived if you assume that r is a function of (x,y,z) with r(x,y,z) = sqrt(x^2+y^2+z^2). In which case, grad r = (x,y,z)/||(x,y,z)||, which we can call r hat.


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I'm trying to get from (13) to (14), here:<br />
<a href="http://mathworld.wolfram.com/Laplacian.html" rel="ugc">http://mathworld.wolfram.com/Laplacian.html</a><br />
<br />
I've managed to show that the first terms equate:<br />
<br />
dg/dr div(grad r) = 2/r dg/dr,<br />
<br />
but I'm struggling to equate the second terms:<br />
<br />
grad(dg/dr) dot grad r = d^2 g/dr^2<br />
<br />
Can anyone spell it out for me please?<br />
<br />
Thank you.
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I'm trying to get from (13) to (14), here:
http://mathworld.wolfram.com/Laplacian.html

I've managed to show that the first terms equate:

dg/dr div(grad r) = 2/r dg/dr,

but I'm struggling to equate the second terms:

grad(dg/dr) dot grad r = d^2 g/dr^2

Can anyone spell it out for me please?

Thank you.

grad(dg/dr) dot grad r = d^2 g/dr^2

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