3D Rotation Along Local Axis (Not Global) Here's the Code. What's wrong?

Question

The following code rotates an object in 3 dimensions:

cosx = Math.cos(radx);
sinx = Math.sin(radx);
cosy = Math.cos(rady);
siny = Math.sin(rady);
cosz = Math.cos(radz);
sinz = Math.sin(radz);

//x-axis
tx = x - cx;
ty = y - cy;
tz = z - cz;
y = (ty * cosx) + (tz * sinx) + cy;
z = (tz * cosx) - (ty * sinx) + cz;

//y-axis
tx = x - cx;
ty = y - cy;
tz = z - cz;
x = (tx * cosy) + (tz * siny) + cx;
z = (tz * cosy) - (tx * siny) + cz;

//z-axis
tx = x - cx;
ty = y - cy;
tz = z - cz;
x = (tx * cosz) + (ty * sinz) + cx;
y = (ty * cosz) - (tx * sinz) + cy;

Since I rotate X first, X turns fine along its axis, but the Y and Z rotate to the global Y and Z instead of their own axes.
However, if I rotate Y first, Y turns fine but X and Z doesn't.
Similarly, if I rotate Z first, Z turns fine but X and Y doesn't.

Any help as to how I can make them relative to each other?
See draw() function in the JS section. Approx line: 160

https://code.sololearn.com/WxtqC6Ji8ZkL/?ref=app

Answer 1

How comfortable are you with matrix notation?

http://paulbourke.net/geometry/rotate/

https://sites.google.com/site/glennmurray/Home/rotation-matrices-and-formulas/rotation-about-an-arbitrary-axis-in-3-dimensions

Answer 2

At once I tried using the matrices to quaternions formula and applying it...in the end after 4 days it failed so I just moved on and now face a new issue (that I'm researching of course)
Frustrum qnd occlusion culling.