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Derivative notation

Let y = f(x). The derivative of f with respect to x is denoted by any of the following expressions:

MATH $\dfrac{dy}{dx}$
MATH MATH

The symbols Dx  and $\dfrac{d}{dx}$ are known as differential operators and are pronounced, the derivative with respect to x of ... The symbols $\dfrac{dy}{dx}$ and $\dfrac{d}{dx}$ are not real fractions---and you can't cancel the d's. The notation, known as Leibniz notation, is a ghost from the past, when the quantities dy  and dx were considered to be infinitely small changes in y and x. Actually, this idea is not so far from our idea of zooming in and computing the slope of what looks to be a straight line.


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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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