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 (2005-09-01 01:13:33)