Derivative Notation: Lagrange, Leibniz, Euler, and Newton

This video goes through the different Derivative Notations that are commonly used throughout Calculus as well as some that are not as common. The four different notations include Lagrange's Notation, Leibniz's Notation Euler's Notation, and Newton's Notation.

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[richardfeynman]

Most physicists that take advanced classes in college are taught Newton's notation and they use it. It's usually neater that the other notations in differential equations of the first and second order.

[jeremyhofmann]

Super helpful because as you learn from different teachers over the years they switch without telling you and you feel like you’ve missed an entire semester by accident.

I’m a programmer by trade so I like to think of all of these as programming statements like diff(expression, respect_to) or diff(expression, respect_to, degree). Then it’s more clear to me on what the math is “doing”.

[sullivan]

Euler notation is the most versatile because it combines concision (not having to write a fraction-like object) with generality. You can easily write single derivatives in any variable to a power (LaTeX: D_x^3 y), or any ordered set of partial derivatives (LaTeX: \partial_{xyz} v). However, it does not have the downside of cluttering the subscript or superscript of the variable itself.

[johnnolen]

The dot notation is common when expressing time derivatives in dynamic systems. It lets engineers know that they're dealing with a derivative with respect to time by inspection.

[SebastianMantey]

Nice overview! I have one question though. Let’s say you have y = f(x) = x². The derivative is then dy/dx = f’(x) = 2x. And now, let’s say you want to know the derivative of y or f(x) at x=6. In Lagrange’s notation you would write f’(6) = 2 * 6 = 12. But how would you write that in Leibniz notation?

My approach so far:
dy/dx when x=6:
dy/dx = 2 * 6 = 12

[pigeonlove]

always wondered why there were so many notations, and if I should change, this explains it, thanks

[luckylukeskywalker]

Thank you very very much for this video, this made me more secure that my collection of different notations (to understand all the stuff my professor‘s writing) seems to be correct. BUT isn‘t it important that the Leibniz notation is the greek d, not a normal d?! I‘ve heard from many different sources that they are critivally different and our lecture also uses them for very different derivative things.

[borisbukalov]

The dot notation is absolutely used in Mechanics!

[a.sh.]

Hey, Prof!
If I had the equation f(x, t) = 2x^2 + t^2
With Leibniz's notation we can get separate df/dx and df/dt.
How would one write this using Lagrange notation (which I, too, prefer)?

Keep up the great videos!

[ronaldt]

super helpful! I was so confused so thank you

[tonymyson]

I'm doing my third year in physics, trust me, you gonna need that newton notation.

[Inventor]

Mechanics uses Newton's notation a lot! But there's a purpose to it all I suppose.

[medotedo]

Hey about Dot Notation if you want to write for higher order it will be the same situation as Prime Notation (Lagrange's) isn't is ? how to do it for forth and fifth derivatives ?

[lordalbert]

Not really. Newton's notation is very common in physics (mechanics)

[alikhanpathan]

on derivative plzz to solve solve some special problems ... and tell us short trick to solve calculus problem

[samisiddiqi]

I honestly prefer the Leibniz Notation because it makes the most sense mathematically, preserving the intuition. Euler's Notation however seems interesting.

[saboo_tage]

Honestly Newton's method was way cleaner than Leibniz' method

[vedarthsharma]

Antiderivative notations in dofferent case

[Autumnrainfall]

Wait I almost exclusively use newtons lol