The Difference Between d/dx and dy/dx

[carultch]

dy/dx is a noun; a thing in an expression or equation, that is a derivative.
d/dx is a verb; a command to take the derivative.

[LudusYT]

Was thinking about doing 100 shorts where I do a different derivative in every short. Should I do it??

[MirorRflction]

This concept becomes especially important in equations with more than just 2 variables. So you can have for example a function y(x, z) with dy/dx and dy/dz, which give two different results from the same primary equation. These are called Partial Derivatives and are very useful in control systems engineering, which is used in nearly all automated tools in factories that mass produce most of our everyday products

[caolanod]

Thanks it's been 25yrs since I took calculus and at the time I didn't understand it.

[yourube]

I always wondered about this but didn't know the Google search term to find out. Now I do.

[RobokiYT]

You are right about that part, infact in calculus this is an essential information, lets say you have y = (2x)/(x^2), you could multiply log on both sides
the equation then would be
ln y = ln 2x - ln x^2, differentiate on both sides and it is a lot easier
and lny differentiation is dy/dx ×1/y, it is kinda hard to understand this step if you don't know chain rule and don't undersyand the logic you just told

[aarongoyvaerts]

Omg, thank you, I have been wondering this for ages!!!

[areeb]

I’m doing further maths in the uk and we have just been introduced to derivatives. This is very helpful!

[Atraments]

I already knew this, but this video managed to finally make implicit differentiation “click” by making me understand why we tack on dy/dx when differentiating y, so that you very much for making this video!

[FndfnnFnefnfn]

Simplier:
d/dx - do derivative of something
dy/dx - do derivative of "y" (specific derivative)

[arthurbraden]

What is insane is that I got an A in Calculus I, II and III but I did not know or remember this. Thank You for going over that simple idea!! :)

[liamconard]

Well said and straight to the point, thanks man!

[dishman]

I learned way later than I should have. Glad I wasn’t alone and that it’s a common thing.

[mpkxi]

You have helped me immensely with this. Thanks a lot.

[alfiehellings]

Both are functions but take different types of input. d/dx takes a function as an input and returns another function, for example x^2 gets mapped to 2x. dy/dx is the output when y gets put into d/dx. It can be viewed as any other real function

[charliemoll]

It took me until late into college to understand this (and I’m a mathematics major). I wish I knew this in highschool!

[apprenticehealer]

Thanks my cousin from 9th grade here in India found it helpful

[johnsonjohnson]

Finally I understand. Thanks for the simple topic but impactful

[mybigbeak]

Took me ages to get this. thanks for making it so clear

[naytte]

There are multiple ways of viewing dy/dx that all produce equivalent results. Leibniz thought of dy/dx as a ratio of infinitesimal changes. Nowadays calculus students are taught that "d" is simply an operator, but honestly that does the intuitive idea behind differentiation a big disservice.