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**KiWoonG****Guest**

hi everyone

i was wandering what

dy

--- meant...

dx

somtimes some other pronumerals are used

for example...

d

---(x^2)

dt

can somebody tell me what these things mean??

Thank you

**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

I may be wrong but...

dy/dx represents y per x.

If y = Miles and X = Hours, it'd be Miles per Hours.

D is probably just a random variable?

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

**dy/dx and dy is another way of representing a function's derivative (in this case, y is the function and the derivation variable is x)**

remember the definition of a function's derivative?

```
f(x+Δx)-f(x)
f'(x) = lim ------------
Δx->0 Δx
```

but

```
f(x) lim f(x)
lim ---- = --------
g(x) lim g(x)
```

so we can put the definition like this:

```
lim f(x+Δx) - f(x)
Δx->0
f'(x) = --------------------
lim
Δx->0
```

now call the numerator "differential in y", **dy**

and the denominator "differential in x", **dx**

as you can see in the above expression, a function's derivative can now be expressed with the help of differentials (infinitely small *increments*)

```
dy
f'(x) = --
dx
```

So as you can see **dy/dx** is the derivative of **y=f(x) with respect to x**

You cand understand this easly if you recall that the derivative of a function is related to the slope of the its tangent line on a certain point. And how do you find slopes? With quotients between the y-increments and x-increments!

The difference is that dy and dx are very small increments.. so small you can only express them using *limits*

...understanding differentials is a major step to any calculus student imho! Then you can move on to more complex topics like integration and **differential** equations.

!)

*Last edited by kylekatarn (2005-08-31 03:13:33)*

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