Yaomomo explains derivatives to Kirishima [Educational]

Kirishima Eijirou

Hey, Yaoyorozu! Got a minute? I'm totally stuck on these derivative problems.

Yaoyorozu Momo

Oh, Kirishima-kun. Of course, I'd be happy to help. What seems to be the issue?

Kirishima Eijirou

I spent so much time working out, I totally forgot about the math test tomorrow!

Kirishima Eijirou

Could you explain derivatives to me? I'll buy you a drink from the vending machine!

Yaoyorozu Momo

There's no need for that, Kirishima-kun. I'd be glad to help you understand.

Yaoyorozu Momo

Let's start with the basics. A derivative measures the rate of change of a function.

Kirishima Eijirou

Rate of change? Like how fast something is moving?

Yaoyorozu Momo

Exactly! Think of it like your training. The derivative would show how quickly your strength increases over time.

Kirishima Eijirou

Oh! So it's like measuring how manly I'm becoming each day?

Yaoyorozu Momo

Well, that's one way to think about it. Now, let's look at the formula...

Kirishima Eijirou

Okay, so the limit as h approaches zero... Wait, what's h again?

Yaoyorozu Momo

H represents a very small change in x. As it gets closer to zero, we get a more precise rate of change.

Kirishima Eijirou

So it's like... measuring the tiniest improvement in my training?

Yaoyorozu Momo

That's a great way to think about it, Kirishima-kun! You're catching on quickly.

Kirishima Eijirou

Ha! Guess all that training is making my brain muscles stronger too!

Yaoyorozu Momo

Now, let's try applying this to a real problem. Can you find the derivative of x squared?

Kirishima Eijirou

Okay, so... I use the power rule, right? The power comes down, and then I subtract one from the exponent?

Yaoyorozu Momo

Excellent, Kirishima-kun! That's exactly right. The derivative of x squared is 2x.

Kirishima Eijirou

Yes! I did it! This is so manly!

Yaoyorozu Momo

Oh my, we've been at this for quite a while. How about we take a short break?

Kirishima Eijirou

Sounds good to me! Thanks so much, Yaoyorozu. You're a lifesaver!

Yaoyorozu Momo

It's my pleasure, Kirishima-kun. I'm glad I could help.

Yaoyorozu Momo

Remember, solving derivatives is just like your training - it takes practice!

Kirishima Eijirou

You're right! I'll keep at it until I master these derivatives!

Kirishima Eijirou

Now, how about that drink I promised you?

Yaoyorozu Momo

Oh, Kirishima-kun, I told you that wasn't necessary...

Yaoyorozu Momo

But I suppose a short break would be beneficial for both of us.

Kirishima Eijirou

Great! Let's go! I'll race you to the vending machine!

Yaoyorozu Momo

Kirishima-kun, there's no need to- Oh, he's already gone.

Yaoyorozu Momo

His enthusiasm really is infectious, isn't it?