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After a night of sniffling over math problems, Armand is a welcome sight in the doorframe of Daniel’s apartment. He looms tall and thin, one leg crossed over the other, curls slicked back and held in place by rosy sunglasses. He removes his gray trench coat and hangs it on the coat rack, one of several small things that Armand introduced to Daniel that make his life that much more luxurious. Daniel also now has a portable steamer for his clothes and coasters for the beer cans that used to sit unbothered on every surface.
Daniel feels too tired to get up, so he simply turns to face Armand and hits him with the most pitiful look he can muster.
“Beloved,” Armand frowns, rushing to his side and holding his face gently. “What’s wrong?”
Daniel sinks into the touch, closing his eyes, as if the math problems will go away if he can’t see them. “I’m gonna fail my calculus test tomorrow,” he sighs, and opens his eyes again. Armand’s face doesn’t look any less grave until Daniel offers him a weak smile. “Professor Atkins is a dick.”
Armand pulls up a chair next to him and peers over the paper, stroking Daniel’s back with his unoccupied hand. “What’s giving you trouble, dear?”
Daniel rests his cheekbone on his knuckles, turning to face him. “I thought I had it until we got to differentiation with multiplication and division,” he laments. “I mean, all the formulas and everything we’re supposed to memorize, on top of remembering differentiation rules.”
Armand holds out his hand, making a grabby motion until Daniel deciphers that Armand wants a pencil. Daniel groans. “Can I have a break, please? I think my brain is melting out of my ears.”
Armand puts the pencil down and strokes Daniel’s jaw. “Sure. A cigarette and a drink always help me think better. You want?”
“Babe, you have the best ideas.”
Armand returns instantly with a pack of Newports and Daniel’s favorite shitty beer, kept slightly chilled by a fridge he had found in a dumpster. While Daniel lights up, holding the lit tip of his cigarette to Armand’s, Armand blushes while he’s reaching for a pencil, which is more than enough motivation to find f prime of a thousand functions.
Armand has already written out the problem Daniel’s struggling with and broken it into small parts. “You did your work wrong here,” he says, pointing with the pencil. “You used the multiplication formula instead of division.”
“Hm?”
“The function is s of t equals t over the quantity of one plus t squared,” he continues. “To differentiate, you need to apply the quotient rule. The prime function of u over v equals u prime times v minus u times v prime, divided by v squared.”
Daniel nods–he’s two-thirds of the way there, and that’s generous.
Armand continues, and Daniel even catches him smiling. Armand’s nerdiness is one of Daniel’s favorite things about him. “You would need to substitute u for t, and v for one plus t squared.” Armand pauses to blow smoke out his nose, and after a trick like that, Daniel could listen to Armand describing paint dry and still hang on his every word. “That’s very sweet, darling,” Armand chuckles. “Hey,” Daniel pouts. “Don’t go using the Mind Gift on me right now. Then you’ll know exactly how little of this I understand and I’ll have to go into exile on a far-away island to avoid humiliation.”
“But beloved, we’re halfway there! You see how I got all this. I may or may not be using the Mind Gift on you right now.”
Daniel huffs. “Go on.”
“U prime is one, and v prime is two t. If we substitute these into the equation, we get one minus t squared over t to the fourth power plus two t squared plus one.”
“Mm-hmm.”
“This means that the equation is f prime of t, or v of t if you’re finding the velocity of s of t. We substitute the numerator, one minus t squared, into the same quotient rule, with the denominator representing v. Can you tell me what u prime and v prime would be in this instance?”
Daniel takes a swig of beer and reaches for Armand’s pencil. “Well, using differentiation rules, v would be four t to the third power plus four t, and u would be two t.”
“Negative two t, but yes, very good, beloved,” Armand purrs, rewarding him with a kiss on the forehead. “So the prime function of s prime of t would be?”
Daniel pauses for a moment, drawing out the unsimplified form. “Well, it’s sort of wordy, but that would be negative two t times the quantity of t to the fourth power plus two t squared plus one, minus the quantity of one minus t squared times the quantity of four t to the third power plus four t, with the denominator being the quantity of t to the fourth power plus two t squared plus one, squared.”
“That’s what the acceleration function would be if we were calculating an object’s position over time,” Armand smiles. “You’re not going to fail the test. You’re going to do swimmingly.”
“Whatever you say,” Daniel sighs, but can’t keep the smile from blooming on his face.