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Simplify[] and Sign[]

I have a handful of 5-variable algebraic expressions that I am pretty
sure have constant signs (I make this assumption based on many tests
using random numbers).  By hand, I've been able to prove that a few of
them do indeed have a constant sign, but the others have eluded me so

Supposing I have, for example, F[w,a,b,c,d,e] = some rational function
in {w,a,b,c,d,e} where the variables w,a,b,c,d,e are strictly
positive.  By hand, I can manipulate some of the partial derivatives
of F in such a manner that I am sure that they have unambiguous signs.
 However, for the rest,

just returns: Sign[D[F,c]] (using c as an example).

My question is two-fold: should I give FullSimplify[] a try in this
case?  or is there a better way of doing this?

If I can somehow "guide" Simplify[] into manipulating these
expressions as I did for the first one then I will be ok.  Perhaps
there is a way to step-through the Simplify[] process?

-Thomas R. Covert

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