you know how slope for a line is (y2-y1)/(x2-x1)? this is usually written as Δy/Δx. But this only works for straight lines; the slope of a curve changes and so to find the slope at a given point, we can’t measure it across any sizeable Δx.

So what do we do? Well some mathematicians back in the day decided to use their imaginations. dy/dx just means, what if we imagine that x2 gets infinitely closer to x1 without actually being x1? This is dx. Then if y is dependent on an equation of x, let’s say y=x^2, what would be then the difference between y2=x2^2 and y1=x1^2? That would be dy.

You have two limits, and you divide 1 over the other (dy/dx) and if your plot has a smooth curve then the limits will solve out to something. Now extend it out to not just this x1 but for all the possible x in your original equation and you get dy/dx = 2x. This function gives you the slope function of your original function, or in other words, tells you the slope of any point on your original curve.

edit: mixed up an x and y, also some clarity