How to force mathematica to take derivatives in a specific way?

I am attempting to take some derivatives of some Lagrange planetary equations. In this I have two types of anomaly which have derivatives that are found geometrically. I’m trying to force mathematica to use the results of these derivatives. I realize that to do this I have defined the derivatives. To get Mathematica to be happy I unprotect D before doing so. Heres my code for that:

Unprotect[D];  D[f, e] := (a/r + (\[Mu]*a)/((\[Mu]*a)^(1/2)*(1 - e^2)^(1/2))^2)*Sin[f]  Unprotect[D];  D[f, M] := (1 + e*Cos[f])^2/(1 - e^2)^(3/2) 

Okay so this is all well. When I evaluate D[f,M] or D[f,e] it seems to work correctly; however when I take the derivatives of other functions derivatives don’t follow those rules I set above. For example, I made up a simple function to check this:

In[58]:= abc [a, e, i, f, c] := e*f*Sin[f]  In[59]:= D[abc[a, e, i, f, c], e]  Out[59]= f Sin[f] 

Uh oh. So my question is how do I get mathematica to match the derivatives I want?

Thanks for all your help

Can you summon a spiritual weapon into the bubble created by Bead of Force? Can whoever is inside cast charm person on someone outside the bubble?

The wording for Bead of Force says "Only breathable air can pass through the sphere’s wall. No Attack or other Effect can." which obviously means that spells such as firebolt or ray of sickness could not harm a creature inside. However, what about spells that only require line of sight?

I’ve read the discourse on Wall of Force, which suggests that you would not be able to do such spells, and the wording is similar to Bead of Force.

When should I have an NPC actively investigate an illusion created by the Phantasmal Force spell?

The phantasmal force spell can be broken if the victim examines the illusion and makes a successful investigation check against the spell’s DC.

What general guidelines should I use to decide when the victim of phantasmal force should use its action to examine the illusion?

Suppose the caster makes an orc think it is being attacked by a wolf.

Should the orc always examine the wolf until the spell ends? Or should the orc use its action to attack the wolf, defend itself, or run away?

Can a space from Phantasmal Force move?

So, my DM is doing a pvp tourney and I am fighting a Mage (5th level) (I am a Shadow Monk and also 5th level by the way). What happened is that in the middle of the fight, the Mage casted Phantasmal Force in me. I failed.

The illusion was of a corridor with one fireball coming of one side, and I, logically thinking, ran away from the fireball and ended up outside the Arena, effectively losing.

The corridor was "infinite" because as I walked the corridor also moved and depht and etc changed to look an infinite corridor. So my question is, this is right? Can the illusion "move" with me? If so, wouldn’t allow the "effective" area of effect way bigger?

Can the Command spell be used to force someone to drink poison?

The Command spell does the following:

You speak a one-word command to a creature you can see within range. The target must succeed on a Wisdom saving throw or follow the command on its next turn. The spell has no Effect if the target is Undead, if it doesn’t understand your language, or if your command is directly harmful to it.

Can the Command spell be used in combat to force a foe to drink poison?

Presumably, the caster would hold out a vial of poison when giving the order.

Does a player know the source of an unseen force attempting [and failing] to act upon their mind? More in description

If a creature attempts to Dominate, deal save-or-suck psychic damage, or otherwise psychologically influence a PC, what do they know about the attempt? Both RAW and opinion answers acceptable, just specify what you’re giving.

Obviously the player themselves know when I ask "Make an x save".

But does the character know? Furthermore, what if it is a visible target. I don’t know if "Mind Blast" is visible, as an example, but ASSUMING it isn’t, say a PC angers a Mind Flayer, and they fail to deal damage to a PC because of a successful saving throw, does the PC know? "The Mind Flayer gives you an unsettling glare. Make an Intelligence saving throw. PC succeeds" Does the character itself know their mind was assailed in some capacity?

Lastly, suppose a PC is immune to a specific effect. I.e. being innately immune to Sleep effects.

Do they know if a creature attempted to use some magical ability to attempt to put them to sleep?

How does Wall of Force interact with objects?

Wall of Force discusses what happens when it goes through a creature’s space:

If the wall cuts through a creature’s space when it appears, the creature is pushed to one side of the wall (your choice which side).

…and I assume similar logic can be applied to small/medium sized objects such as chairs that can be moved.

But what about objects that are not a creature, or a single creature, and aren’t particularly mobile?

For example:

a) An enemy is hanging from a rope. Mage casts a horizontal Wall of Force that "cuts" through the rope.

b) A Chain Devil has grappled the fighter from 10′ away with its Chain attack that has 10′ reach. Mage casts Wall of Force between them as part of a hemisphere, hoping to cut the chain and trap the devil.

If the object was a stone wall, I think most would agree that the stone wall stops the Wall of Force as the panels wouldn’t be contiguous or the sphere wouldn’t be able to expand in a direct line from its point of origin.

Does something as thing as a rope or chain have a similar effect?

Could the area of a Wall of Force be greatly reduced just by having streamers hanging from the ceiling, or standing in a forest with a bunch of tall trees?

Can the Mirror of Life Trapping force multiple saves?

The Mirror of Life Trapping can trap creatures in it.

Any creature other than you that sees its reflection in the activated mirror while within 30 feet of it must succeed on a DC 15 Charisma saving throw or be trapped, along with anything it is wearing or carrying, in one of the mirror’s twelve extradimensional cells.

Does it force multiple saves? If someone stares at the mirror a remains there looking at themselves for 5 minutes, do they have to save more than once? Or only every time they blink?

What if they look away and look back on the mirror?

What is “Force” Damage?

From what I can find in answers like this and this, force damage is a nebulous concept of “pure magical energy”, which isn’t very helpful in answering the question of “what effect does this attack have on the creatures I hit with it?”

Even different spells with the same damage type of “force” have different effects. For example, I usually describe magic missile as the enemy being hit with three (or more) bludgeoning attacks. Disintegrate, on the other hand, still deals force damage but explicitly says that if it reduces them to 0 hit points, they are completely disintegrated.

This problem is in effect at least a small amount with Radiant as well, but Acid, Cold, Fire, Lightning, Thunder, Necrotic, Poison, and any others I forgot are relatively easy to imagine with their effects on living beings.

So.. what is Force damage?