pi x is simply a constant pi multiplied by x.

It’s pi when you differentiate it, similar to other constants.

why is it not pi/pix tho, as the rule says its differentiate/copy
kind of confused with this topic even for exponential and trigonometric differentiation ....

Because we are simply differentiating a constant multiplier of x.

Saying that d/dx (pi x) = pi / pi x is like saying that d/dx (5x) = 5 / 5x, which is not correct.

But if you are talking about d/dx ln (pi x), then yes, it’s pi / pi x.

Unfortunately, we are doing the differential of ln (pi x - 6x2).

The rule for this says that differentiate this entire function f(x) gives

1 / (the function in the brackets)

times the differential of the function in the brackets.

So d/dx ln (pi x - 6x2)
= 1 / (pi x - 6x2) times the differential of (pi x - 6x2)

Because the thing inside the bracket is not just pi x, but the entire (pi x - 6x2).

ohh so for the numerator, its just differentiating pix-6x^2 alone so the ln differentiation rule is not applied and normal differentiation rule is applied instead? the denominator will be just copying pix-6x^2

Yes

thx :)