First try : ?date?., third attempt 06Sep2015, rev1 24Sep2015, 
  09Jan2016 rev4Lucas4-15, 22May2016 used my expression from file 
  "Howell - Background math for Lucas Universal Force, Chapter 4.odt" HFLN format :

#  Start with (4-15) Howell's version
   E,B for symmetry point charge @v_const 
   Adapted non-[derivative, integral] form of Amperes law  
/$   Bi(ro - vo*t,t) 
   = vos/c*Pph
     * [  q*sinOo*ros/|rov - vo*t|^3   
        +   sinOp*|Ei(ro - vo*t,t)|  ]   
/*   taking the ∂/∂t of (4-15) Howell's
/$1)   dp[dt : Bi(ro - vo*t,t)] 
     = vos/c*Pph
       * [   dp[dt : q*sinOo*ros/|ro - vo*t|^3 ]  
            + dp[dt :   sinOp*|Ei(ro - vo*t,t)| ]  ]  
/*
yy)"Pseudo-constant variables/expressions" within partial derivatives wrt time 
yy)Remove : [c,L(v),v,b,q,rp,|ro - vo*t|^(n),Op,sinOp,Pp] - Chap4 v=constant, Chap5 v=variable.
yy)Retain : [t,E,B,ro,Oo,sinOo] are the key variables to retain within derivatives
   for Chapter 4 verifications 
# yielding
/$2)   dp[dt : Bi(ro - vo*t,t)] 
     = vos/c*Pph
       * [  q /|ro - vo*t|^3 *dp[dt : ros*sinOo ]
           + sinOp            *dp[dt : |Ei(ro - vo*t,t)|]  ]   
/* From "Howell - Key math info & derivations for Lucas Universal Force.odt" 
	Section II.4 : 
/$II.4.9)  dp[dt : ros*sinOo] = 0
/*OOOPPPS!!! -  q term drops out as it is a constant 
  and the derivative is zero
/$     dp[dt : Bi(ro - vo*t,t)] 
     = vos/c*Pph
       * [  q /|ro - vo*t|^3 *dp[dt : ros*sinOo ]
           + sinOp            *dp[dt : |Ei(ro - vo*t,t)|]  ]   

/*10Jan2016  The problem here is that in (4-14) and (4-15) the "q" expressions are constant - leading to a zero derivative.


dp[dt : ros*sinOo] = vos*sinOo*(cosOo - 1)
/*therefore : 
/$4)   dp[dt : Bi(ro - vo*t,t)] 
     = vos/c*Pph 
        * [  q/|ro - vo*t|^3 *vos*sinOo*(cosOo - 1)
           + sinOp*dp[dt : |Ei(ro - vo*t,t)| ]  ]  
      = vos/c*Pph 
        * [  q*vos*sinOo*(cosOo - 1)/|ro - vo*t|^3   
           + sinOp*dp[dt : |Ei(ro - vo*t,t)| ]  ]  
/* This is very different from Lucas, at least in appearance.


/*++++++++++++++++++++++++++++++++++++++
/*add_eqn  "Possible_Lucas_error_or_omission    
	04_16rev4Lucas4-15
	E,B for symmetry point charge @v_const 
     Derivative form of Amperes law  

/$		∂[∂(t): Bi(r - v*t,t)]  
		= vs/c*Rocs(POIo)*sin(θ)*φ´hat* 
			[  3*q*vs/c*(Rocs(POIo)*cos(θ) - vs*t)/|r - v*t|^5 
			 + 1/Rocs(POIo)/c*∂[∂(t): |Ei(r - v*t,t)|] ] 

/%		dp[dt : Bi(ro - vo*t,t)] 
		= vos/c*Pph 
		 * [  q*vos*sinOo*(cosOo - 1)/|ro - vo*t|^3 
			 +       sinOp *dp[dt : |Ei(ro - vo*t,t)|]  ]   

/* Note how different my version is  ??!!??
/%		∂[∂(t): BTpdv(POIo(t),t)] = ∂[∂(t): BTodv(POIo,t)]  
		=   Vons(PART)^2/c*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))*Rodh(Vonv_X_Rpcv(POIo))  
		 *{   3*Q(particle)  /Rpcs(POIo(t),t)^3  
			 -    EIpds(POIo(t),t)/Rpcs(POIo(t),t)   
			 -  ∂[∂(t): EIpds(POIo(t),t)]/Vons(PART)/cos(Aθpc(POIo(t),t))  
		  }  

/*	10Jan2016  OOOPPPSSS - q-term is zero (constant has zero derivative)
	09Jan2016 WRONG! :  I use Op not Oo for 2nd term RHS (as with (4-15), different terms  
		This could partially be due to differentiation, but not all.   
	??It seems to me that Lucas has dropped the "Vons(PART)*cos(AOpc(POIo,t))*EIpds(POIo,t)/Rpcs(POIo(t),t)" term.
		But there should be an EIpds(POIo,t) term!

/*	It seems clear to me that Lucas has : 
- dropped the "Vons(PART)*cos(AOpc(POIo,t))*EIpds(POIo,t)/Rpcs(POIo(t),t)" term. But there should be an EIpds(POIo,t) term!
		22Aug2019 NO!???  I factored out Vons(PART)*cos(AOpc(POIo,t))  ??? 
- has too many "c"s
		22Aug2019 - do dimensional analysis!!
- has the term "(ros*cosOo - vos*t)/|ro - vo*t|" in the first term in parenthesis.  
- I have NO real idea of why the (ros*cosOo - vos*t) pops up anyways, and why the cos term all of a sudden (spherical coords does not explain this!)

30Mar2018 do spherical coordinate derivative!?!!
NOTE!!! : use "/media/bill/SWAPPER/Qnial/MY_NDFS/matrix derivatives in [cartesian, cylindrical, spherical] coordinates.ndf"