Can't plot derivative of Hankel function

Question

I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a real variable and $i = \sqrt{-1}$ is the imaginary unit.

According to the chain rule, it should be:

$$\frac{\mathrm{d}}{\mathrm{d}(ix)} \left[ H^{(1)}_3 (ix) \right] = \frac{1}{i} \frac{\mathrm{d}}{\mathrm{d}x} \left[ H^{(1)}_3 (ix) \right]$$

So, first, I defined:

a[x_] := HankelH1[3, I*x];

It is a real-valued function and it's easy to plot, for example with Plot[a[X], {X, 0, 10}].

Then:

b[x_] := D[a[x], x];

which is pure imaginary and should represent $\displaystyle \frac{\mathrm{d}}{\mathrm{d}x} \left[ H^{(1)}_3 (ix) \right]$. Then,

c[x_] := D[a[x], x] / I;

should be $\displaystyle \frac{\mathrm{d}}{\mathrm{d}(ix)} \left[ H^{(1)}_3 (ix) \right]$ and should be real.

However, I can't plot it:

Plot[c[X], {X, 0, 10}]

gives

General::ivar: 0.0002042857142857143` is not a valid variable.
General::ivar: 0.20428591836734694` is not a valid variable.
General::ivar: 0.40836755102040817` is not a valid variable.
General::stop: Further output of General::ivar will be suppressed during this calculation.

Why? What am I doing wrong?

I'm using Mathematica 12.0.0 on Linux x86 (64 bit).