Leibniz notation

[ewr...@gmail.com]

What does the d stand for in d/dx? 

[William DeMeo]

The notation "d/dx" consists of four formal symbols that, taken
together, stand for the differentiation operator. These symbols don't
really have any meaning taken separately. That is, (d/dx)f means the
derivative of the function f with respect to x, but the d or the dx in
d/dx do not have any formal meaning.

Having said that, you can informally give an interpretation to these
symbols as follows: in "dy/dx" the "dx", which is sometimes called the
"differential of x", can be thought of as an infinitessimal change in
x. So, "dy/dx" represents the change in y per infinitessimal change
in x. You can also think of dy/dx as representing "rise" (dy) over
"run" (dx).

So, to get back to your question, what does the "d" stand for? It
doesn't stand for anything by itself, but you can think of it as the
"differential operator". When d "acts" on some variable or function,
say, x, then we get dx which represents a small change in x.

But for now you should not think of these symbols separately, but
should take them together---that is, d/dx is an operator that acts on
(differentiable) functions and gives the instantaneous rate of change
of the function.

On Sun, Feb 22, 2015 at 11:50 AM, <ewr...@gmail.com> wrote:
> What does the d stand for in d/dx?
>

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[ewr...@gmail.com]

Wow, looking back on this comment!  I just finished calc 3 today, meaning that I got through the whole book in a year.  I feel like a new person.  I remember the first month of calc 1 being abstract and somewhat frustrating.  I didn't know where it was going or why it was important, but I knew that it was weird and somehow worked.  I could rant for hours, but I just wanted to say that I was taught really well back in the first semester.  Looking back to calc 1, there was a lot of foreshadowing to the second and third semesters.  I remember one problem in class where we had to differentiate something like ten times in a row and ended up with a factorial.  Then in calc 2 BAM Taylor series and Euler's identity.  Talk about goose bumps. The way that derivatives and integrals generalize to higher dimensions in calc 3 is beautiful as well.  Oh man don't get me started on the connectedness between calculus, physics, and my other classes.    

Thank you Iowa State math department for opening me up to the wonderful world of math!!