dy/dx, d/dx, and dy/dt - Derivative Notations in Calculus

This calculus video tutorial discusses the basic idea behind derivative notations such as dy/dx, d/dx, dy/dt, dx/dt, and d/dy.

Derivatives - Fast Review:

Introduction to Related Rates:

Derivative Notations:

Related Rates - The Cube:

__________________________________
Inflated Balloon & Melting Snowball:

Gravel Dumped Into Conical Tank:

Related Rates - Area of a Triangle:

Related Rates - The Ladder Problem:

Related Rates - The Distance Problem:

____________________________________
Related Rates - Airplane Problems:

Related Rates - The Shadow Problem:

Related Rates - The Baseball Diamond Problem:

Related Rates - The Angle of Elevation Problem:

Related Rates - More Practice Problems:

_________________________________
Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[xVENx]

you probably already know it, but man, at any point in your life when you feel down remember that you are the man who helped millions over the internet for free, you are a good man!

[liamtolkkinen]

My calc professor never covered this, she just expected us to understand what the difference was! This video was a huge help so I thank you for clearing it up for me!

[MuhNine]

I have taken University Calculus 1 and 2 and this has always confused me. Whenever I'd ask a teacher they would just say its the derivative of y in respect to x but that means nothing! This video has finally made me understand something that I just had to guess at for over 2 years of calculus and almost a full year of calculus based physics

[kiranlalani]

this is saving my life during online school where you don't learn shit

[Zersara]

*The first few seconds already taught me more than my teachers ever could*

[Chris-pthh]

I'm at one of the top universities in the world, and your videos are what really teach me. Once I'm out of med school, you're getting a fat donation.

[nyuhsexecutioner]

Just wanna say...





You saved my life on my high school days and im very grateful for that ^_^ *thank you*

[markchen]

My German physics professor just "blitzed" through everything without talking about this. You just saved my life! Thanks a lot.

[matheuscastello]

i wish my teachers explained it this concisely, i never knew what to do when i saw dy/dx and now i know! thank you very much

[shamsideenjamiu]

You deserve some accolades sir because you really know how to explain stuff honestly, you make maths look like a piece of cake. Love all the way from Nigeria 🇳🇬❤

[minleyfox]

This is a good explanation but is missing something that produces confusion among the comments.
It is correct that d/dx (y^3) = 0.
It is in general also correct that d/dx (y^3) = 3*y^2 dy/dx. However, it should be clarified that this notation only "works" if y is a function of x.
Thus, it should be better written as: d(y(x)^3)/dx = 3*y(x)^2 dy(x)/dx.

[ArtiMishra-rdcp]

You read my mind. I was thinking about this today and you posted... I am glad I found you early. I am just in 11th std

Love from India 🇮🇳

Thank you for your gr8 work

[zojirushi]

Thanks that first part was very helpful I was always curious to know the difference between dy/dx and d/dx.
Now I know dy/dx tells us what the answer is and can also be written as y' and f'(x).
While d/dx is telling us to differentiate inside brackets.

[EpicTurbulance]

Thank you, you have really helped make Calculus look easier. We don't really go through this in Education. And the fact you use dy/dx instead of f' and g' helps me understand too. Now I know why d/dx is written and have learned better about how derrivatives with respect to a specific variable.

[kiyoponnn]

Whenever I watch your videos, my anxiety just fades away

[josesousa]

I am not even learning this at school I just like his voice

[ahmedreda]

Man, God bless you! I have just started my master's this semester, and one course is all about derivative notations. AND I ALMOST DIDN'T UNDERSTAND A THING UNTIL I WATCHED YOUR VIDEO! SO THANK YOU SO

[umagovindarajan]

Thanks a lot.. I'm an Indian here in India for many highly tough competitive examination exams like
JEE, NEET these are concepts are most important and play a vital Once again thank you so much for explaining this clear.... 🤗🥺❤❤❤

[jeremyhofmann]

It helps me to translate these notations into programming language statements. So dx/dy could be called with differentiate(x, y) where differentiate(expression, respect_to) is a function that accepts an initial expression and applies the “respect to” variable to each differentiated term in the expression.

[degenerationz]

Dy/dx --> denotes a derivative of the function y with respect to x.

D/dx--> states that you should take the derivative of the function in the proceeding adjacent parentheses.

Dy/dx=d/dx (y)