I am assuming that the 'd' in dx/dy stands for differentiation
Not quite. Let the value of a property y depend on the value of another property x. Example, the amount of water in a bath (let's call it y litres) depends on the time (let's call it x minutes) for which the water has been running
Calculus is based on the properties of the way in which the value y changes as the value of x changes. As a rate , this is expressed as:
not: y/x, but: change in y divided by change in x,
and this can be written as: Δy/Δx
But when Δy and Δx approach 0, then
the increment of y / increment of x is written as dy/dx.
In calculus we need to work this out for small changes in x and y, and the shorthand is to say
the infinitesimal increment of y /the infinitesimal increment of x, and this is expressed as the ratio dy/dx.
That is, in the Differential Calculus, the increment of x and y is very small, theoretically equal to infinitely small, what we call infinitesimal. You can't measure it, but the ratio is real and measurable.
So d is not differentiation per se, but the way of indicating the infinitesimal increment in the value to which it s tagged.
In the example given, dx might be 0.0000001second, and dy 0.000001ml. Not tangible numbers.
But their ratio is 0.6 ltr/minute.
BTW, another shorthand for dy/dx is f'
This is useful where in more complicated maths, you need to write say d/dx.(dy/dx) this can be written f²(y)