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Chapter 5: Chapter 5: The Vanishing Derivation Process

Old Yang’s full name was Yang Shengguo, and he was already thirty-eight this year.

Watching Li Dong’s chalk fly across the blackboard, he suddenly felt a sense of unreality.

In that instant, it was as if he saw his younger self.

Back then, he had been studying for his bachelor’s and master’s degrees at Beijing Normal University. Full of vigor and ambition, he was on a natural path to pursue his doctorate and walk the road of scientific research.

But at the critical moment of publication, his research findings were stolen by the very mentor he respected and published under someone else’s name.

He felt wronged. He was young and hot-headed, unwilling to bow down, so he confronted his mentor and caused a huge scene.

As a result, not only were his hopes of a Ph.D. dashed, but he was effectively blacklisted from that circle, unable to find even a decent job.

His heart had grown cold by then, so he returned to his hometown of Jiangcheng and became a math teacher at the ordinary, public Seventh Middle School.

In the first few years, he had also wanted to teach these kids well. He wanted to teach them knowledge, but more than that, he wanted to teach them how to be good people.

He wanted to teach them how not to be taken advantage of, and how, if they ever became teachers themselves, to never exploit their own students.

But reality was never as rosy as one imagined.

Every place has its own rules. The top-quality students were all snatched up by the prestigious private schools and key public high schools.

The students who came to Seventh Middle School were, for the most part, ordinary people with average abilities. Some were still trying hard but couldn’t find the right method, stuck in mediocre limbo. Others had already given up completely, planning to just coast their way to a high school diploma.

Watching them, Yang Shengguo’s passion slowly cooled.

’Just teaching is enough. As long as I can face my conscience and share what I know... as for whether the students listen or learn anything, that’s up to fate.’

He had thought this was all his life would amount to—just watching over his thermos of goji berry tea, slowly growing old here.

Until today.

Li Dong, the student who usually couldn’t even touch the passing line, had given him a sudden shock—and a long-overdue surprise.

At this moment, Li Dong’s eyes were fixed solely on the problem on the blackboard.

He was incredibly focused now. The complex function graphs before his eyes were breaking down, one by one, into their smallest components.

’No need to brute-force the derivative’s zero point...’

’For a problem with this structure, the key is to observe its form.’

’Since the problem requires the inequality to hold true for all values, I just need to find the critical point where the graphs of the functions on both sides are tangent. That will give me the limit for the constant *a*.’

He found that Joule’s ”decomposition method” was incredibly useful. Once you saw through the core Logic, the rest was just grunt work.

Although, this grunt work was a bit demanding.

He was actually still struggling a bit. First, his Concentration was only at 0.1, so it was easy for his mind to wander during high-intensity mental calculations.

Second, his logical reasoning was still at 0, the level of an ordinary person. If he hadn’t already done a problem with the same core principle, he might not have been able to solve this one so quickly.

Thankfully, his natural Memory was 0.1, which saved him from having to look up formulas in a book.

Li Dong picked up the chalk. Facing the modified problem Old Yang had given him, he didn’t perform any complex derivative calculations, nor did he draw any coordinate axes.

”Solution: The original equation is equivalent to e^x ≥ a ln(ex).”

Li Dong’s hand paused for half a second.

Then, he directly skipped the entire process of constructing functions, taking second derivatives, and discussing extreme points—a process that would have filled half a draft notebook for an average student.

Two fundamental tangent line inequality models appeared in his mind.

He wrote two lines of extremely concise derivation on the blackboard:

”Using tangent line scaling, we know: e^x ≥ ex and x ≥ ln x + 1.”

”Therefore: e^x ≥ ex = e(x) ≥ e(ln x + 1) = e(ln x + ln e) = e ln(ex).”

When this chain of inequalities appeared on the blackboard, the pen in Misha’s hand CLATTERED onto her desk.

”Is this... double scaling?”

Misha’s face was filled with disbelief.

Old Yang was also stunned. That leap showed real depth. Without a massive amount of practice and extremely high mathematical intuition, no one would dare to write it like that.

But he could see that the logical chain within it was flawless.

”From the inequality chain above, the equality holds if and only if x=1.”

”Thus, a_max = e.”

The chalk made a final, crisp sound against the blackboard.

”Um... Teacher Yang, I’m done.”

The classroom was so quiet you could hear a pin drop.

The students looked at each other in confusion. They couldn’t really understand the solution on the board and had no idea if it was correct.

So they could only turn their gazes to Old Yang.

A few students in the front row, including Misha, were frantically verifying the solution in their notebooks.

”How... how did he get to this step?”

A student mumbled under their breath.

”Where’s the differentiation process? Why did he just use a greater-than-or-equal-to sign?”

”Yeah, isn’t that taking too much of a shortcut?”

Old Yang stood where he was, staring at the solution on the board, and said nothing for a long time.

After a long while, he let out a deep sigh, as if expelling years of pent-up frustration.

’Looks like... I can’t just coast and wait to die anymore.’

His voice was so soft that no one heard him.

Old Yang didn’t rush to judge whether the answer was right or wrong.

For the vast majority of students in Class 2 of the third year, this ”isomorphic scaling method” was a competition-level technique. There was no need to delve deep into it.

It was better for them to secure their fundamental points rather than waste time on this technique.

”Li Dong, you...”

Just as Old Yang was about to speak, a knock suddenly came from the classroom door.

KNOCK KNOCK KNOCK.

The door was pushed open, and a somewhat weary face peeked in.

”Teacher Yang, sorry to interrupt. I just need to make a quick announcement.”

Old Yang nodded toward the door.

”Go ahead, Teacher Jiang.”

Teacher Jiang addressed the students below the podium.

”Everyone, sorry for the interruption.”

”The city just sent out a notice. Next month, there’s a Commercial Physics Cup competition, which is a qualifier for the provincial preliminaries.”

”The school has been allocated a few spots. Any students interested in signing up? There’s no training; just think of it as practice.”

The class fell silent, everyone burying their heads even lower.

Teacher Jiang was used to this. These tasks to fill quotas weren’t common at Seventh Middle School, but they weren’t rare either.

Students from their school usually went just to fill seats. They weren’t really qualified to truly participate.

”If anyone wants to sign up, come find me in my office next Monday.”

After speaking, he gave Old Yang a wry blink.

The meaning was clear: *Nothing I can do. We’re short on people.*

Yang Shengguo nodded and watched Teacher Jiang leave.

After this brief interlude, the classroom returned to silence.

Yang Shengguo turned around and gave Li Dong a deep look, his tone much softer than before.

”Alright, Li Dong, you can go back to your seat.”

Being stared at by Old Yang made Li Dong’s skin crawl. He couldn’t shake the feeling that there was something strange about the look in his teacher’s eyes.

”Oh.”

Once Li Dong was back in his seat, Old Yang pointed to the blackboard and said,

”Li Dong’s solution to this problem is... completely correct.”

”Furthermore, his approach was very clever, using the scaling method. It seems he’s put in a lot of hard work on his own time.”

Old Yang paused, then changed his tone.

”However, this method requires a very high level of logical thinking and is prone to errors. Everyone should proceed according to their own abilities.”

”In the college entrance exams, these types of problems are usually bonus questions. We should still focus on securing the points we’re supposed to get and not bite off more than we can chew.”

Although Old Yang was trying to cool things down, the way the students looked at Li Dong had already changed.

Surprise, suspicion, jealousy... a mix of all kinds of emotions.

”Didn’t Li Dong fail math? How did he suddenly...”

”Did he just memorize the solution to this hard problem to show off?”

”Probably. Why else would he not even calculate the derivative?”

In the front row, Misha bit her lip, still furiously scribbling derivations in her notebook.

Even using the approach Li Dong had provided, she had only just managed to verify the validity of the first inequality.

’Those steps he skipped... was it really because they were too simple for him?’

Misha glanced back at Li Dong, a faint sense of defeat creeping into her heart.

...

The bell for the end of evening self-study finally rang.

It was Friday, so boarding students could leave school and go home.

Many parents were waiting for their children at the school gate.

Li Dong walked toward the bus stop with his backpack on, Liu Liang silently following beside him.

Just as they were about to get on the bus, Liu Liang suddenly spoke up. ”Dongzi.”

”Hm?” Li Dong stopped walking.

Liu Liang looked at him, his expression complex. Half-joking, half-serious, he said,

”Did you really get hooked on studying?”

Li Dong could hear the trace of dejection in his tone.

During your teenage years, when a friend you always messed around with suddenly starts trying hard, that sense of panic from being left behind is unavoidable.

Li Dong turned around and said with sincerity,

”Liangzi, I think we need to start being responsible for our future.”

”I want to give it my all, if only to make my mom worry a little less.”

Liu Liang was stunned for a moment, then broke into a grin to hide the loneliness in his eyes.

”Look at you, all enlightened now. Go on, go on, future top student.”

After saying goodbye to Liu Liang, Li Dong got on the number 302 bus home.

It was already past ten at night, and the bus was empty.

Li Dong sat in a window seat.

Outside the window, the nightscape of Jiangcheng receded before his eyes.

The skyscrapers in the city center were brightly lit. The price of a single square meter there was equivalent to his family’s entire monthly income, assuming they didn’t eat or drink.

The bus slowly pulled away from the commercial district. The lights grew sparser, and the surrounding buildings became low and dilapidated.

Li Dong’s hand tightly gripped the phone in his pocket. It held the key to changing his destiny.

The bus stopped at the entrance to his old residential complex.

Li Dong climbed the six flights of stairs with his backpack on. Before he even opened the door, he could hear his mom, Li Qin, talking on the phone inside.

”...Alright, alright, thank you for the trouble.”

”Ah, as long as it helps him improve his grades, that’s all that matters. Besides, it’s much cheaper than hiring a professional tutor... Okay, tomorrow then. Thank you so much.”

Li Dong pushed the door open and went inside.

Li Qin hung up the phone and saw her son had returned.

”Xiaodong, you’re back! Are you hungry? I can heat up some food for you.”

”I’m not hungry.” Li Dong changed his shoes and looked at his mother.

”Mom, who were you on the phone with just now?”

Li Qin poured him a glass of water and said with a smile,

”Oh, I have something to tell you.”

”One of my colleagues has a kid who goes to Jiangcheng University of Technology. He’s a junior in the math department.”

”I heard his grades are pretty good, so I asked him to come over on weekends to tutor you.”

Afraid her son would resist, Li Qin quickly added,

”He’s a university student, so he’s cheaper. We can afford it.”

Li Dong froze.

Jiangcheng University of Technology was a local Tier 2 university. A math major from a Tier 2 university... well, those who know, know.

’A student from a Tier 2 university’s math department is going to tutor me?’

Li Dong subconsciously touched his phone.

Who were his ”teachers” now?

They were Isaac Newton and James Joule—some of the most brilliant stars in human history!

It felt like he was enjoying a gourmet feast, but his mom, afraid he was hungry, had specially hired someone to give him a couple of cold steamed buns.

He really wanted to refuse, but seeing his mother’s excitement,

he couldn’t turn down her good intentions.

Ever since his father passed away, his mother had shouldered the burden of their family all by herself.

Now, she was pinching pennies to hire a tutor for him. If he refused, it would make her feel like she hadn’t provided him with the best learning conditions.

So, Li Dong nodded and said,

”Okay.”

”Don’t worry, Mom. I actually really love the feeling of studying now.”

Hearing this, Li Qin’s face blossomed into a wide smile.

”Yes! That’s the spirit!”