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#1 2005-08-31 01:12:35

KiWoonG
Guest

C a l c u l u s

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

#2 2005-08-31 01:29:05

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

Re: C a l c u l u s

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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#3 2005-08-31 02:50:19

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

Re: C a l c u l u s

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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