Thanks anuttarasammyak
So what you are saying that moving the dx/dt in and out of the d/dx() operator is valid ?? that's to say
$$\frac {d(\frac {dy} {dx})}{dx} \cdot \frac {dx} {dt} =\frac {d(\frac {dy} {dx}\cdot \frac {dx} {dt})}{dx}$$
??
I don't think so .. what i mean by $$\frac{d}{dx}(\frac {dy} {dx})$$ is $$\frac {d (\frac {dy} {dx})} {dx}$$
i think this is what you were pointing to ? sorry if i missed something else