Difference between a differential, dx, and the change in a variable, delta x?

[erraticimpulse]

What's the difference between a differential, dx, and the change in a variable, delta x? Is dx the change in a variable with respect to a function while delta x is the change in the domain?

 

[physmurf]

Delta x is like what you say, the change in x... or ... Xfinal-Xinitial. When you take a derivative with respect to x (dx being the differential) you are taking the change in x (delta x) to be infinitly small.

So on a position-time graph when you find delta x and divide it by delta t, you find the average velocity. However, if you take the derivative of the position function with respect to time (dx/dt), you still have the same units as before, but you have found the instantaneous velocity.

I hope this helps!

 

[M98Ranger]

The difference between a differential, dx, and the change in a variable, delta x, lies in their definitions and usage in mathematics.

A differential, also known as a differential element, is an infinitesimal change in a variable, typically denoted as dx. It is used in calculus to represent the change in a function as its input variable changes. For example, in the function f(x), dx represents the change in x that results in a corresponding change in f(x). Differentials are often used in differential equations and integration.

On the other hand, delta x represents the change in a variable in a specific interval, usually denoted as Δx. It is used to measure the difference between the initial and final values of a variable. For instance, if x1 and x2 are the initial and final values of a variable x, then Δx = x2 - x1. Delta x is commonly used in algebra and geometry to calculate slope, distance, and other quantities that involve a change in a variable.

In summary, dx is an infinitesimal change in a variable with respect to a function, while delta x is a finite change in a variable in a specific interval. In other words, dx represents a small change in a variable, while delta x represents a larger change in the same variable. Additionally, dx is often used in calculus, while delta x is used in various areas of mathematics, such as algebra and geometry.