Derivative of an interpolation function is noisy

Question

I have a set of numerical data of 1501 points, in the form of $\{x_i,a_i\}$ which I uploaded to here and here.

I need to compute the numerical derivative of this data. In particular, I need the quantities

\begin{equation} C=\frac{1}{\left| \frac{da}{dx} \right|}, \hspace{1cm} D = C' = \frac{dC}{dx} \end{equation}

To do this, I interpolated the data given in the link,

data = Get["https://pastebin.com/raw/Ccvm7Bgp"];
Interp = Interpolation[data];
Plot[Interp[x], {x, 0, x[[1501]]}, PlotRange -> All]

Then I computed C by

DInterp[x_] := Interp'[x];
C[x_] := 1/Abs[DInterp[x]];

But DInterp and, consequently, C (shown below) are very noisy, let alone sC'$:

This is the derivative of the interpolation, Dinterp

This is C

How can I solve this? I need to determine $C$ and $C'$ very precisely, how to I get rid of the noise to achieve this?