# 7a. The Differential

## Integration Mini Video Lecture

The differential is an essential piece of the integral calculus puzzle. This video explains what they are.

## Video transcript

[Music...]

### What is a differential?

Well its no big deal really. But it is important in the understanding of integration.

A differential is just like a derivative except we write it across the page.

Let me illustrate, if I start with *y* equals 3*x* to the power of 4, the derivative, *dy* over *dx* is equal to [four 3s are] 12*x* to the power 3. `(dy/dx = 12x^3)`

Now this is a derivative, to write it as a differential, all I have to do is this: *dy* equals 12 *x* cubed *dx*. And I've written it in this form, *dy* equals the derivative expression 12*x* cubed *dx*. `(dy = 12x^3dx)`

That's all there is to it really, what we do later is we use it in integration.

What you'll see later is we'll have the integral of say 12*x* cubed *dx*. `(int 12x^3dx)`

This is the proper way to write an integral, integral sign, and then a differential. Hopefully it will become clearer the more examples that you see later.

[Music...]

### Search IntMath, blog and Forum

### Online Calculus Solver

This calculus solver can solve a wide range of math problems.

Go to: Online algebra solver

### Calculus Lessons on DVD

Math videos by MathTutorDVD.com

Easy to understand calculus lessons on DVD. See samples before you commit.

More info: Calculus videos

### The IntMath Newsletter

Sign up for the free **IntMath Newsletter**. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!