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de.riv.a.tive

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"Um, senpai?" Kaidoh hovered in the doorway to the chemistry lab, staring awkwardly at his feet. Inui blinked, carefully set down the beaker of bubbling poison-green liquid he was examining, and removed his goggles.

"How can I help you, Kaidoh?"

Kaidoh fixed his gaze even more intently on his scuffed-up sneakers. He needed to go shoe-shopping soon. "You said, if I ever had trouble with my math homework..."

"Of course!" Inui beamed behind his improbably opaque glasses. "And I have just the thing - Inui Juice Super Special Calculus Remix!"

Kaidoh's head shot up, and the faint blush lingering on his cheeks quickly faded to white, and then continued straight to pale green. "Ah, no, senpai, that's okay," he said hurriedly, preparing to flee.

"Joke, Kaidoh. It was a joke." Inui pretended not to notice how Kaidoh sagged against the doorframe in relief. His juices were very effective! He didn't understand why only Fuji ever wanted to try them. "What topic are you covering in calculus?"

"Integration." Kaidoh stepped into the lab hesitantly, aware that he was entering a dangerous domain. "I didn't do well on the last test."

"Well, why don't you show it to me, and we can see where you went wrong," Inui said cheerfully as he cleared a space on the lab bench. Kaidoh dug in his bag for a moment and produced a sheet of paper, liberally covered with markings in red ink. Inui took it and frowned. "Kaidoh, I know math is not your strongest subject, but thirty-one out of a hundred is..."

"The teacher said I could make it up tomorrow," Kaidoh said, going red again. "So I need to study."

"All right." Inui glanced at the glaring red 31 one last time, then shook his head and returned his attention to Kaidoh. "So what about integration is giving you trouble? I know you understand derivatives just fine."

"I wasn't really paying attention when the teacher introduced this unit, senpai," Kaidoh said humbly. "Maybe you could just explain the whole thing?"

"Well, a derivative is the slope of a line, right? And an integral is the area under it. So if you take the integral of a derivative, you should come back to the original function, the line. So you're trying to see what the function you have is the derivative of. Let's start with a simple function, 3x^2..." Kaidoh's eyes glazed over, and he settled down at the workbench, resting his chin in his hand as he listened to Inui's voice without paying the slightest bit of attention to what he was saying.

Inui frowned, taking in Kaidoh's rapt inattention, and decided to test a theory.

"...so then you multiply everything through by three, factor the polynomial and take the second derivative of the remainder. Why don't you give it a try?"

Kaidoh blinked away his blank stare, took the example Inui had blatantly failed to do anything mathematically feasible to, and integrated it perfectly. Inui looked at the test again, and noticed that every single problem had been integrated properly. Kaidoh had then filled in all the constants - wrong. Then Inui reflected back on the past week, which he had spent cooped up in the chemistry lab trying to refine a new Inui Juice Remix, and considered the possibility that Kaidoh was maybe a little justified in using trickery to get his attention. When he really thought about it, it was pretty flattering - Inui didn't know that he would have sabotaged his own calculus grade for anything or anyone.

"Well, you seem to have a better grip on the concept now," Inui said diplomatically.

"Yes, thank you, senpai," Kaidoh agreed politely, eyes wide and guileless. "You explain things much better than Homura-sensei."

This was actually true in a general sense, Homura-sensei being a mathematical genius but completely incapable of basic human communication, so Inui let it pass. "Would you like to go for a run when you finish your studying?"

"Yes," Kaidoh replied instantly, and went dull red. Inui smiled at him reassuringly (or as reassuringly as Inui could, given that all of his expressions ended up looking threatening; Kaidoh understood the sentiment, at least) and started putting away his chemistry equipment. Doubles partner > chemistry experiments, Inui decided. It was one mathematical expression he should have no difficulty remembering.