Whats the derivative of a differential? D_x ( dx ) ?

>>9154834
Huh? You mean like a second derivative? Or are we running the speed of differential equations here?

Used as a noun in this context as a noun I can only take "differential" to mean a distance, so its derivative would, of course, be 0.

>implying f(x)=dx has any meaning whatsoever

>>9154937
[math] y = dx \iff \frac{1}{y} = \frac{1}{dx} \iff \frac{dy}{y} = \frac{dy}{dx} \iff \log y = y [/math]

And as we know the equation [math] log y = y [/math] has constant solutions in the complex numbers. Once of which is approximately [math] -0.3 + 1.3i [/math] So one solution is the function [math]f(x) = -0.3 + 13i [/math]

>>9154960
What? How does solving y=dx have anything to do with the manipulation (specifically taking the derivative) of the function f(x)=dx? The fact that y=dx has constant and discrete solutions shows you can't even take a derivative, as derivatives necessitate continuity.

how you do define the differential?
Usually you take the tangent space of your functional space and define it as a vector with some properties.
The bummer is that your point is fixed due to choosing your sistem of coordinates (maps on the manifold).
So defining the derivative of a differential as a limit is quite nonsense, because you can't define properly $df(x+\delta)-df(x)/\delta$, because the charts are different.
What mathematicians do is defining the differential operator d that is akin to differential of a function, expanding on a tensor product of TM with the properties of a derivative operator.

>>9154834
Dx*dx
dx^2
the differential of a constant is zero so is dx^2

>>9154937
fix dicks.

https://en.wikipedia.org/wiki/Exterior_derivative
d(df)=0 for all smooth f

>>9154834
Take a look at fractional calculus.
https://en.wikipedia.org/wiki/Fractional_calculus

There are things like half derivatives. Gamma functions show up.

You could probably differentiate with respect to the fractional parameter.

>>9154834
Depends on your space metric function.

>>9154960
this is really sad