Differential D

[Arrow_Raider]

In calculus, stuff like dy and dx pops up a lot. I've tried to understand it, but I just can't seem to figure out what the d is supposed to represent... is it supposed to be derivative of [variable]?

[krtxmrtz]

In calculus, stuff like dy and dx pops up a lot. I've tried to understand it, but I just can't seem to figure out what the d is supposed to represent... is it supposed to be derivative of [variable]?

The d is used as a notation to indicate a very small amount or increment.
dx means a very tiny increment of the variable x and the same applies to dy. Look at the function plots that usually illustrate the definition of derivative in any calculus book.

[oswaler]

The d represents delta which in turn represents a tiny change. The basic premise of calculus is that any curve will look like a straight line if you examine a tiny enough section of the curve. When you are calculating an integral you are trying to find the area under a curve. The way this is done is by cutting the space under the curve into very, very thin rectangles. The height of each rectangle is determined by evaluating the function at a specific value on the x axis. The width of the rectangle is the distance of the change on the x axis when calculating each rectangle. In practice the change on the x axis would have to be a finite number, but in calculus analysis it is assumed that the change on the x axis is infinitely small.

so when you see dy/dx it refers to the tiny change to the outcome of the equation on the y axis that will be caused by making a tiny change on the x axis.

Remember the slope you learned in algebra. dy/dx represents the slope (y2-y1)/(x2-x1).

-Eric