Quote by danne89
Hey! How's about the second derivate in this notation. Is this right:
[tex]\frac{d(dy/dx)}{dx} = \frac{ \frac{d(dy)}{d(dx)}}{dx} =\frac{d^2y}{d^2y} \frac{1}{dx}= \frac{d^2y}{d^2dx^2}[/tex]

No.It should be:
[tex] \frac{d}{dx}\frac{dy}{dx}=\frac{d^{2}y}{dx^{2}} [/tex]
Your notation makes no sense.
The derivative of "n"th order wrt to "x" of the function "y" in the notation of Joseph Louis Lagrange is
[tex] y^{(n)}(x) [/tex]
In the notation of Gottfried Wilhelm Leibniz the same "animal" is
[tex] \frac{d^{n}y(x)}{dx^{n}} [/tex]
and it can be seen as appying the operator [itex] \frac{d}{dx} [/itex] "n" times on the function "y(x)".
Daniel.