' - - File: Identities3
'    Given a constant, two functions,F.& G, and a vector, A.
a = .2845E-1
F{t} = Sin[t^2 - a]^2 + 1/t                              ' t <> 0
G{t} = Sqrt[F{t} + t^2 + a]                             ' t > 0
P{t} = F{t} * G{t}

Pd{t} = Diff[P,t]                                              ' dP/dt  = d (F{t} * G{t}) / dt
Fd{t} = Diff[F,t]                                               ' dF/dt
Gd{t} = Diff[G,t]                                             ' dG/dt

Sp{t} = F{t} * Gd{t}  +  Fd{t} * G{t}               '  F{t} * Gd{t}' + F{t}' * G{t}  = dP/dt ?
'To determine if they are numerically the same, find their difference, if any.
D{t} = Abs[Sp{t} - Pd{t}]                                  ' Without regard to sign.

' *******************************************************************************************
' Does (F{t} * A<t>)'  =  F{t} * A<t>' + F'{t} * A<t>  ?

A<t> = <Sin[t], Cosh[t]^2, Log[t^2 + a]>
C<t> = vMpy[F,A]                                           ' F{t} * A<t>; Recall--parmeters not in vector Math.
Cd<t> = vDiff[C]                                             ' d(F{t} * A<t>) /dt
Ad<t> = vDiff[A]                                             ' A'

Sa<t> = vAdd[vMpy[F,Ad], vMpy[Fd,A] ]     ' F{t} * A<t>'  +  F{t}' * A<t>
' - - - - - - - - - - - - -  OR - - - - - - - - - - - - -
Sb<t> = vAdd[vMpy[F,vDiff[A]], vMpy[Fd,A]]  ' Same as Sa; Cannot use Diff[F,t] here
'                                                                            ' becaue no parameters in vector math.
Sd<t> = vSub[Cd,Sa]                                    ' Difference about zero?
<t = 1.6548>

