delta y vs. dy (differential)

We will discuss the difference between delta y and dy. Delta y is the difference between y-value value and the original y-value. But dy is the differential and it's an approximated difference between the y-values.
For more calculus tutorials, please check out my just calculus channel @bprpcalculusbasics

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@blackpenredpen

[richardaversa]

For those not aware, what he described is essentially Linear Approximation, or Linearization

[johnchristian]

I like these in depth videos, they make you appreciate math more, as apposed to how you learn in high school just rushing through memorizing formulaes and rote learning solutions. Great video!

[asadashoori]

I finally found out what exactly differential is. I've searched on the internet, read books for a few weeks but I couldn't find a tutorial as simple as yours. I'm gonna pray for you. Thank you so much.

[drachaksakcha]

> ∆y is exact change

that would explain why I never have any ∆y when I go to the coffee shop

[Gaark]

and now I finally understand why there's a 'dx' tacked on the end of the dif'd function :D thanks!

[randomeggthatworksforthefb]

Holy moly this was so much better than my professors explanation! He literally was trying to explain the concept using marble and bread.

[benburdick]

This can be a great introduction into Euler's method as well!

[animalfarm]

Interesting, I always understood dy/dx only existed on the limit as Δx approached zero. Anything else was just delta Δy/Δx. ie dy/dx=lim Δx→0 Δy/Δx.

[lucarosolem]

Mate, thank you a lot. I've been reading James Stewart's book for over an hour trying to understand what you've simplified in 10 minutes.

[error]

Just did a calc midterm and this video would've bumped me up from a 70% to an 80%. For the sake of future math tests, you will be my new professor!

[anjanasahu]

With the god pen switching technique he also writes so fast that I didn’t see him writing 7:04 “just an approximated”
A man with so much talent !

[saranikolic]

Thank you so much!
I'm rewatching this video after 6 months. The idea is very clear, and the explanations were understandable. This helps me a lot.
♥

[HaloWolf]

Haven't took an intertest in Math ever, even when I was doing this in school.

I always came across the Delta symbol in Wiki articles whenever I was looking up information. This defined it quite well.

[MarcoYeungChannel]

This makes my concept clear now! Thanks

[aubreydosto]

I watched your video to learn actually but I suddenly smile when you're looking and smiling at the camera. How cute of you💕

[smrtfasizmu]

This channel is fantastic, I thought that dx and dy were delta x and delta y when delta x approaches zero. That they really make sense only when they are divided by each other and that we can sometimes use them separately but that was just a math trick. Apparently, dx and dy are not necessarily going to zero, they are just delta x and delta y of the tangent line which is determinate by the derivative. The only thing is that ratio dy/dx has to be equal to the ratio of delta y/delta x in the limit when delta x - >0.

[saeedgul]

Impressed with the way you explained such a technical concept with sweet and smiley face
Thanks

[hoteny]

Thanks. My math teacher just wouldnt tell me what the heck was a dx or dy or d in general (only told me it was differential)

This was a good explaining

[alegian]

I love how you show real uses of theoretical calculus. Liked 😉

[domrushton]

Thanks mate by far the easiest explanation vid I have found on YouTube. You must be a great tutor 👍