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The product rule applied to the curl takes the form
(here f is a scalar functions and the product
here is ordinary multiplication of f with each component of
v or of An important consequence of this rule is that a vector
that points in the radial direction that is a function only
of the radial variable has 0 curl where it is differentiable.
This is true whether the radial variable is r or Exercise 17.4 Find the curl of |
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.)
.
It follows because the second term is zero for vectors (x,
y, 0) and (x, y, z) while the first term will be 0 when both
vectors in it point in the radial direction which will be
so when f is a function only of that variable.
which is a unit vector in the 
direction