Re: d/dx Can someone tell me where this notation originated from and why it is in this form (fraction)?

Question

For example I worked this out on my own. Can someone tell me if this is correct, preferably refer me to a web site that has a concise description of where it came from.

f(x)=x^2
d f(x) = d(x^2) dx
d f(x) / dx = d(x^2)

were d means the derivative
Is this right?

Answer 1

Since it is called Leibniz notation, I assume Leibniz invented it or at least made it popular.

http://en.wikipedia.org/wiki/Leibniz_notation

Answer 2

It comes from the definition of a derivative as "change in y divided by change in x", or delta(y)/delta(x) (in the limit as delta(x)->0). However, delta represents finite differences; while the derivative refers to infintesimals. To make this distinction, "d" is used instead of delta:
dy/dx. When y is a function it is written (d/dx)[y]. It really is a fraction.

Your equations are all correct except the last, you left out /dx: should be d f(x) / dx = d(x^2) / dx

Answer 3

sorry - your three lines' logic does not seem to be good.
dx is a notation that represent a very small gap of interval on the x axis.
d itself does not come from the word derivative, bu from that dx approach - indeed the derivative of a function is defined as the limit value of the fraction :
(f(x)-f(x+dx)) / dx
when dx becomes very small.
so in the notation df/dx, the d is related to the difference f(x)-f(x+dx) ...