i was wandering what
somtimes some other pronumerals are used
can somebody tell me what these things mean??
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?
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.
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
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)