What exactly allows a differential relation form of an equation?

[rexregisanimi]

What exactly allows a "differential relation" form of an equation?

I understand this in a superficial way but I'd really like some more clarification. If anybody can provide a little better understanding on this subject, please feel free to post anything at all. Even a sentence or two would be helpful.

I am reading through the optics section of my Stellar Astrophysics book and I came across the following sentences:

Using the small-angle approximation, tan(θ) ≈ θ, for θ expressed in radians, we find

y = fθ.​

This immediately leads to the differential relation known as the plate scale, dθ/dy,

$\frac{dθ}{dy}$ = $\frac{1}{f}$.​

What I don't completely understand is how and why one can simply go from the y=fθ form to the dθ/dy = 1/f form. I understand what the equation means but I don't understand the rules behind switching from one form to the other. Are there any or can I change any two variables to differential form to get a new relation? Any help or guidance at all would be appreciated.

 

[Mandlebra]

For f not a function of y or theta,

dy= fdθ

Then its just symbol pushing.