Is it possible to not differentiate through an undefined variable?

Suppose I have some $ \lambda$ that is a function of $ x$ , and I don’t know exactly what it is yet.

Then, doing the following differentiation D[lamb, x] gives zero. But what I really want is to not have Mathematica evaluate the expression, i.e., just leave it as it is until I know $ \lambda$ later.

Is there a way to achieve this? Thanks!

Does the bonus action shove from Unearthed Arcana’s Telekinetic feat move the target through the air, or only on the ground?

Imagine a party of PCs exploring a dungeon inside a volcano. After a climactic confrontation with the Big Bad, the volcano begins to erupt, and the PCs must flee for their lives. Unfortunately, one of the PCs — Tarly Target — is badly injured and can barely walk. Working together to carry Target, the PCs race toward the volcano’s mouth. Just as freedom nears, a sudden quake tears open the path before them, creating a 15-foot chasm that begins filling with molten lava. There’s no way Target can make the jump.

Psimon Psion, a PC with the Telekinetic feat from Unearthed Arcana’s "Psionic Options Revisited", proposes to use the feat to try to hurl Target across the chasm. The feat’s third bullet says:

As a bonus action, you can try to telekinetically shove one creature you can see within 30 feet of you. When you do so, roll your Psionic Talent die, and the target must succeed on a Strength saving throw (DC 8 + your proficiency bonus + the ability modifier of the score increased by this feat) or be moved toward you or away from you a number of feet equal to 5 times the number you rolled. A creature can willingly fail this save.

Assuming Psion could roll a 3 or greater on his Psionic Talent Die, sufficient to move Target the full 15 feet required to clear the chasm, is this a viable use of the feat? Must Target remain in contact with the ground the entire time he’s being moved by the shove, such that he’d immediately plunge to his doom once moved over the chasm? Or can the shove actually propel him through the air to the other side?

For completeness’s sake, I note the following:

  • The normal shove action (PHB p. 195-196) only moves a creature a maximum of 5 feet, so it does not offer much guidance here.
  • The telekinesis spell (PHB p. 280-281) can move a creature, but the move is not characterized as a shove and explicitly can hold the target in mid-air, so it is not helpful here either.

Can you identify telepathically received messages sent through spells like Sending as magical via Detect Magic?

An enemy casts Sending to communicate with a player from far away. In this example, the player character doesn’t know anything about the Sending spell and he might think he is just hearing voices or going crazy.

Another player casts Detect Magic to scan the area. Can this player detect the presence of the telepathic message inside the first players head via Detect Magic as an evocation spell.

Does failing to tumble through an occupied space end your action?

One Tumble skill use requires a check (DC 25) to do this:

Tumble at one-half speed through an area occupied by an enemy (over, under, or around the opponent) as part of normal movement, provoking no attacks of opportunity while doing so. Failure means you stop before entering the enemy-occupied area and provoke an attack of opportunity from that enemy. Check separately for each opponent. Each additional enemy after the first adds +2 to the Tumble DC. (Player’s Handbook 84)

Abe the Medium human rogue is 10 ft. from his opponent, Bob the Medium human fighter who wields a longsword. Abe takes a move action and uses 10 ft. of his speed 30 ft. to become adjacent to Bob. Then Abe makes a Tumble skill check as described above to move through Bob’s space, fails the Tumble skill check, provokes an attack of opportunity from Bob, and stops before he enters Bob’s space.

Does Abe’s failed attempt to enter Bob’s space flat-out end Abe’s move action? Or does Abe’s failed attempt to enter Bob’s space consume 10 ft. of Abe’s speed, and Abe can spend his remaining 10 ft. of speed as he wills? Or does Abe’s failed attempt consume none of Abe’s speed—as Abe didn’t actually enter Bob’s space after all—, and Abe can spend his remaining 20 ft. of speed as he wills? Or is there another outcome that I’ve not listed here?

Does the Voice of the Chain Master eldritch invocation let me cast a purely verbal spell through my familiar?

In D&D 5e, as a Pact of the Chain Warlock, I can choose an eldritch invocation that lets me speak in my own voice through my familiar called Voice of the Chain Master (PHB 111):

You can communicate telepathically with your familiar and perceive through your familiar’s senses as long as you are on the same plane of existence. Additionally, while perceiving through your familiar’s senses, you can also speak through your familiar in your own voice, even if your familiar is normally incapable of speech.

Healing word is a spell with only a verbal component (PHB 249):

Components: V

[…]

A creature of your choice that you can see within range regains hit points equal to 1d4 + your spellcasting ability modifier.

The description of verbal components in the rules of spellcasting (PHB 203) says the sound of my voice alone is what causes the magic of this spell to happen:

Most spells require the chanting of mystic words. The words themselves aren’t the source of the spell’s power; rather, the particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion.

Say my familiar is in another room, no matter how far away. Through my familiar’s eyes, I see a target at 60 feet. From my familiar comes my own magic-infused voice. That particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion that travel to the target and heal it.

Is this possible?

An archer firing through an arrow slit has improved cover. Do his targets have cover?

I’m running a module that features a fort with arrow slits and murder holes, and I’m trying to figure out what the cover rules are for people on each side of them.

Under the Combat rules, the CRB states:

Improved Cover

In some cases, such as attacking a target hiding behind an arrowslit, cover may provide a greater bonus to AC and Reflex saves. In such situations, the normal cover bonuses to AC and Reflex saves can be doubled (to +8 and +4, respectively). A creature with this improved cover effectively gains improved evasion against any attack to which the Reflex save bonus applies. Furthermore, improved cover provides a +10 bonus on Stealth checks.

From this, it seems clear that the defending archers should have improved cover. This is reinforced by this section under Dungeon Environments:

Walls with Arrow Slits

Walls with arrow slits can be made of any durable material but are most commonly masonry, hewn stone, or wood. Such a wall allows defenders to fire arrows or crossbow bolts at intruders from behind the safety of the wall. Archers behind arrow slits have improved cover that gives them a +8 bonus to Armor Class, a +4 bonus on Reflex saves, and the benefits of the improved evasion class feature. (emphasis added)

The words "defenders" and "behind arrow slits" make me think that the cover is at least somewhat directional – the defending archers are meant to be at an advantage over the besiegers (which makes sense). However, the general cover rules seem to suggest that the besiegers might also have some cover:

Cover

To determine whether your target has cover from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target’s square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the target has cover (+4 to AC).

When making a melee attack against an adjacent target, your target has cover if any line from any corner of your square to the target’s square goes through a wall (including a low wall). When making a melee attack against a target that isn’t adjacent to you (such as with a reach weapon), use the rules for determining cover from ranged attacks.

I think that the intent is that arrow slits would be at the corners of grid squares. RAW, I think that would give the besiegers no cover. However, on the map I’m using, the arrow slits are in the middle of the grid squares, which suggests that the besiegers also have at least cover, if not improved cover.

Distinct from this question (although related) in that this is about improved cover like arrow slits, whereas that was more a case of low cover.

Can you use the Diplomat feat through your Familiar with the Voice of the chain Master?

So the Feat goes:

If you spend 1 minute talking to someone who can understand what you say, you can make a Charisma (Persuasion) check contested by the creature’s Wisdom (Insight) check. If you or your companions are fighting the creature, your check automatically fails. If your check succeeds, the target is charmed by you as long as it remains within 60 feet of you and for 1 minute thereafter.

Can a player trigger this effect through a familiar when he speaks through it? I don’t want to deny my player this "because I said so," but it totally breaks any notion of balance for him to (for instance) send his familiar to god knows where, find someone important, pretend to be a great wizard trapped in a pseudodragons body, charm them through diplomat, then make them do god knows what.