# Divergence Operator Binding?

1. Mar 26, 2012

### victor.raum

I'm reading about the transport theorem in my vector calculus book. They state the following at the beginning of the section:

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Let F be a vector field on R^3. Let c(x, t) denote a flow line on F starting at location x and continuing out for t seconds. Let J(x, t) denote the Jacobian of c with respect to x, and with t fixed. We then have

dJ/dt = [div F(c(x, t))] * J

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Now, what confuses me is the [div F(c(x, t))] part. Does that mean the divergence of F evaluated at c, or does it mean the divergence of of the composite function (F o c)? In other words, how tightly does the divergence operator bind to its operand?

Expanding out dJ/dt piece by piece tells me that the statement in question should read "the divergence of F evaluated at c." I am pretty sure I did the expansion correctly, but I would still be curious to hear someone else chime in.

P.S. Apologies for not TeXing any of this post. I only know Plain TeX, but my understanding is that the forums here only accept LaTeX.

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