Is dy/dx a fraction?

Is dy/dx a fraction?
This question was asked by Mahir. Hopefully this video answers your question.

[khairolhazeeq]

Dresses like Pikachu
*Uses Doraemon Song*

[blackpenredpen]

dy/dx is not a third grade fraction, it is a “calculus fraction”!

[shaochen]

dy/dx isn’t a fraction... Or is it?
*VSauce Music plays*

[blackpenredpen]

Pikachu + Doraemon music



Life is good

[Vincentsgm]

bprp : ofc i will not eat the whole pizza tonight
me:

[crashcoptr]

I saw the poll for this yesterday, and I was super excited for this video. Thanks BPRP!

[nishaindace]

My friend : dy/dx is a fraction
Me: you are not a joker .You are the entire circus.

[TSPxEclipse]

10 minutes summarized:
Q: Is dy/dx a fraction?
A: No, dy/dx is a ratio of two unlike but related things; all fractions are either quotients or ratios, but not all ratios are fractions and all quotients are fractions.
Ex 1. 5 mph is a ratio of 5 miles to (per) 1 hour, it cannot be thought of as 5 miles out of 1 hour. It simply wouldn't make sense.
Ex 2. Spending $75/$100 is quotient representing the idea that $75 out of $100 was spent, it cannot be thought of as the ratio $75 to $100; in this case this would be saying there are $175 total, which is wrong.

[youknowwho]

People before learning calculus: I have no idea why calculus is so hard, just cancel the d in d/dx to get 1/x

People after learning calculus: FML

[benjaminwalters]

Ok but how in the world did you predict 1/e

[rodwayworkor]

You see, before today, I knew level 1 calculus and, just to understand your videos, I learnt from Product Rule, Quotient Rule, Chain Rule to Harmonic Series to Ratio Test in 3 hours. Must be the most divine part of my life. Writing, as soon as I completed Ratio Test.

[obinnanwakwue]

If someone looks like a Pikachu and talks like a Pikachu, then does it make him a Pikachu?

Not always. It could be a Ditto. It could be a clone created by Mewtwo.

[johannesmoerland]

Locally, dy/dx behaves like a fraction; and assuming that dx is infinitesimally small, one can formally write dy=m*dx; and because m is a constant, integrating results in y=m*x+c, which is the linearisation/first order Taylor series expansion of the function at a given point. However, one should be careful when doing so as infinetisimal calculus (treating dy/dx like a fraction) is not without contradictions

[garykwok]

Oh!!! Thank you for this video!! In fact I have the same difficulties in learning calculus at first when being told that dydx is not a fraction. But it works like a fraction!! Your video is so helpful to me, a graduate student who has done tons of calculus questions, but still, don’t understand the meaning of dydx.

[qillerdaemon]

I heard that business about dy/dx not being a fraction during my first calculus class ("you can't separate the dx from the dy!"), then saw several years of math, physics, and chemistry professors operate it exactly as if it were a fraction. Just like you did at 9:20. Had once, just once!, one of them had suggested it was a *ratio* and not a fraction, I would have understood it fine. But no one ever did, and I just sat confused the whole time.


This reminds me of when you added two integrals together, and I sat flabbergasted over the fact that you just did, while I had years of math teacher tell me "it's improper to do algebra on integrals..." Yet you did and it was perfectly legitimate!

[JJPMaster]

this needs to become the “send this to your crush without context” video of the math community

[ninjan]

I noticed BPRD never truly justified why dy/dx is a ratio, other than just saying "it doesn't make any sense" and proclaiming that dy/dx is similar to a ratio though analogy - that is not a proof that it isn't a fraction. All fractions can be expressed as ratios, and saying dy/dx can be expressed as a ratio or that it is similar to one doesn't rule out the possibility that dy/dx is a fraction. Change my mind

[AK-tcxp]

What's sad about the Indian education system is that it has equipped me to evaluate complex integrals, solve hard differential equations, without actually understanding what dy and dx are.

[Blockster_cz]

I didn't understand the explanation with graphs, but the part with ratios really got me. It's such a perfect way to show that even though something looks like a fraction, it isn't a fraction.

[jayamitra]

That fraction explanation reminds me of the half derivative Peyam did... 1+1=2 😂😋