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Re: Differentiation problem/bug?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg69789] Re: Differentiation problem/bug?
*From*: dimmechan at yahoo.com
*Date*: Sat, 23 Sep 2006 04:44:23 -0400 (EDT)
*References*: <eevrea$gfd$1@smc.vnet.net>
Hi.
I cannot explain you why D[inp, r, NonConstants -> {F}] fails.
I suppose because in the definition of inp there is no explicit
presence of r. This idea came considering the example from
the Mathematica book
D[x^2 + y^2, x, NonConstants -> {y}]
2*x + 2*y*D[y, x, NonConstants -> {y}]
I guess someone more experienced than me will give a better
explanation or maybe he will succeed in applying the option
NonConstants -> {F}.
Options[D]
(Information[Evaluate[#1[[1]]]] & ) /@ %;
{NonConstants -> {}}
"NonConstants is an option for D which gives a list of objects to be
taken to depend implicitly on the differentiation variables."
Attributes[NonConstants] = {Protected}
Anyway you can work as follows:
inp = 1/4 + 3/(8*E^((2*I)*F)) + (3*E^((2*I)*F))/8 - E^((-2*I)*F -
I*Î¸)/4 + E^((2*I)*F - I*Î¸)/4 - E^((-2*I)*F + I*Î¸)/4 +
E^((2*I)*F + I*Î¸)/4 + E^((-2*I)*F - (2*I)*Î¸)/16 + E^((2*I)*F -
(2*I)*Î¸)/16 + E^((-2*I)*F + (2*I)*Î¸)/16 +
E^((2*I)*F + (2*I)*Î¸)/16 - 1/(8*E^((2*I)*Î¸)) - E^((2*I)*Î¸)/8;
g[r_] := inp /. F -> F[r]
Here is the derivative you are looking for
FullSimplify[D[g[r], r]]
((-(1/8))*I*((-1 + E^(I*Î¸))^4 - E^(4*I*F[r])*(1 +
E^(I*Î¸))^4)*Derivative[1][F][r])/E^(2*I*(Î¸ + F[r]))
And here is the antiderivative of the last result
Integrate[%, r]
(1/16)*E^(2*I*(Î¸ - F[r]))*((-1 + E^((-I)*Î¸))^4 + E^(4*I*F[r])*(1 +
E^((-I)*Î¸))^4)
Finally, here is the verification
FullSimplify[g[r] - %]
Sin[Î¸]^2/2
The function and the indefinite integral w.r.t. r of its derivative
w.r.t. r differ a constant w.r.t. r function as it should be.
Regards
Dimitrios Anagnostou
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