131: Chapter 131 I didn't bring my book

To be honest, the feeling Shen Qing gave him had always been a bit "distant."

It wasn't the distance of intentional alienation, but rather a kind of innate aloofness that instinctively made people hesitant to get close.

Since the start of the semester, the two of them hadn't even had a proper conversation.

Therefore, Chen Fan didn't have a deep impression of her, nor could he say he understood her.

Seeing Shen Qing look over, Chen Fan smiled politely.

She withdrew her gaze without any expression.

He didn't mind and was just about to take out his book when he reached into his bag—it was empty.

He had forgotten to bring it.

He looked around; the people nearby were either strangers or busy with their own things. He had no choice but to let his gaze fall back on Shen Qing.

There were a few minutes left before class, and the teacher hadn't arrived yet.

The students around them were either looking down at their phones or chatting in small groups, but Shen Qing was quietly looking at the Advanced Mathematics textbook in front of her, as if everything around her had nothing to do with her.

"Shen Qing." Chen Fan called out in a low voice.

Shen Qing looked up, a hint of surprise in her eyes; she didn't seem to expect Chen Fan to take the initiative to call her.

"I didn't bring my book." Chen Fan said briefly.

Shen Qing glanced at him, her eyes holding an ambiguous meaning, as if saying, "Why did you come to class if you didn't bring your book?"

However, she didn't say anything; she just pushed the textbook toward him, placing it between them.

As she leaned in, Chen Fan caught a faint scent, the fresh fragrance of shampoo, without any trace of perfume. It smelled very clean.

"Thanks." He said.

Shen Qing didn't respond, her gaze already back on the textbook.

The bell for class rang, and the Advanced Mathematics teacher walked in with books tucked under his arm. His hair was combed meticulously, and his eyes behind his glasses were very bright.

He put down the books, scanned the classroom, and picked up the roll sheet.

"Let's take attendance first."

The classroom quieted down. The teacher called out names one by one, and whoever was called would raise their hand and answer.

"Chen Fan."

"Here." Chen Fan raised his hand.

The teacher looked up at him, seemingly a bit surprised—he probably didn't expect Chen Fan to appear in the classroom today.

After roll call, the teacher opened the textbook and turned to write a function on the blackboard: f(x) = sin(x²) · e^x.

"In the last lesson, we covered the differentiation of composite functions, and in this lesson, we will continue from there." He picked up the chalk and tapped the blackboard. "For this problem, don't rush to calculate it; let's take it step by step. When differentiating composite functions, first break down the outer layer, then multiply by the derivative of the inner layer. In this problem, the outer layer is a product, so first use the product rule…"

The chalk scratched across the blackboard. The teacher spoke at a steady, unhurried pace, explaining everything from the product rule to composite functions, and then to the specific steps of differentiation. The problem was broken down clearly, and the dense chalk writing covered half the blackboard.

Ten minutes later, he put down the chalk and turned to face the class.

"Do you understand?"

A scattered response came from below: "Understood—"

The teacher nodded and wrote another one on the blackboard: "f(x) = arctan(ln√(1+x²))."

"Who can explain how to solve this problem using the method I just taught?" The teacher turned around and scanned the classroom.

Seeing no one answer, the Advanced Mathematics teacher picked up the roll sheet on the table and started calling names.

"Zhang Yiwei, you come up."

Zhang Yiwei stood up and stared at the blackboard for several seconds, his lips moving as if he were still calculating silently, but he delayed in stating a complete step.

"First, take the innermost… no, that's not right. First, let u equal…"

"Let what equal?" The teacher pressed.

Zhang Yiwei was completely stuck, his face flushed red. He gripped his pen, standing there unable to advance or retreat.

The teacher waved his hand to let him sit down and scanned the classroom again: "Who else knows? Come up and try."

His gaze swept from left to right, finally resting on Chen Fan.

As for Chen Fan, a student who frequently skipped class, he had made up his mind from the beginning—if he continued to skip class, he would definitely make him fail the course this semester.

Regardless of how high your college entrance exam score was, if your attendance rate wasn't enough, you had to fail.

But a while ago, the Dean of the School of Management had specifically spoken to him.

He said that because of his startup, Chen Fan really couldn't guarantee normal attendance, and he hoped he could be flexible and try not to let him fail.

At first, he was hesitant. After all, he was from the School of Mathematics, and he was teaching a public course to students of Business Administration. It wasn't the same system as the School of Management, and the Dean couldn't control him.

But Zhang Mingyuan was a Vice President after all, so that meant he could control him. He had no choice but to agree.

Furthermore, Dean Zhang had told him one thing—Chen Fan guaranteed he could rank in the top three of the class in the final exam.

This remark made him change his mind a little. If Chen Fan could really rank in the top few, then the issue of absenteeism could indeed be discussed.

So he set a line in his heart: top five would do; it didn't have to be top three. As long as he could rank in the top five, the matter of absenteeism would be wiped clean.

If he couldn't achieve that, then he shouldn't blame him for being heartless.

However, since Chen Fan dared to make such a bold claim, he also wanted to test what the student's level really was.

How could he guarantee he would rank in the top three if he frequently didn't attend class?

"Chen Fan, come up and solve this problem."

The classroom quieted down, and everyone's gaze fell on Chen Fan.

Even Shen Qing, who was beside him, turned her head and glanced at him expressionlessly. There was no mockery in her eyes, but no expectation either.

On the contrary, the surrounding students looked at Chen Fan with a hint of pity in their eyes.

In their view, for someone who frequently skipped class to be called up to solve a problem, the result would most likely be standing on the podium in embarrassment.

Chen Fan, however, didn't care about the surrounding gazes at all. Not to mention that he had already mastered all the subjects of the freshman year, even if he hadn't and couldn't answer, it wouldn't affect him.

He stood up, walked to the podium at an unhurried pace, and took the chalk handed over by the teacher.

On the blackboard was the problem the Advanced Mathematics teacher had just posed:

f(x) = arctan(ln√(1+x²)), find the derivative.

Chen Fan glanced at the problem, the chalk hovered for a second, and then he began to write.

The first step: let v = ln√(1+x²) = ½ ln(1+x²). His handwriting was clean and crisp, without the slightest hesitation.

The second step: the derivative of v = x / (1+x²).

The third step: the derivative of the original function is 1 / (1+v²) · v' = 1 / (1+¼[ln(1+x²)]²) · x / (1+x²).

The last step: simplify to x / [(1+x²) (1+¼(ln(1+x²))²)].

He put down the chalk; the whole process took less than two minutes.

The teacher stared at the blackboard for a few seconds and couldn't find any faults. The steps were clear, the simplification was spot on, and the answer was correct.

"Can you explain your problem-solving process?" He spoke up.

Chen Fan didn't hesitate; he turned around to face the classroom. His voice wasn't loud, but it was clear enough.

"This problem is a three-layer composite function. The outermost layer is arctan, the middle layer is ln, and the innermost layer is √(1+x²). When differentiating, break it down layer by layer from the outside in, and multiply by the derivative of the inner layer at each step…"

He spoke quickly, but his logic was extremely clear. Why he did it at each step and what needed to be paid attention to in the middle were all explained clearly.

The classroom was very quiet, and even those people in the back row who usually played games during class looked up.

After finishing, Chen Fan put the chalk back into the tray and returned to his seat.