I just think of the definition of a derivative.

d is just an infinitesimally small delta. So dy/dx is literally just lim (∆ -> 0) ∆y/∆x. which is the same as lim (x_1 -> x_0) [f(x_0) - f(x_1)] / [x_0 - x_1].

Note: ∆ -> 0 isn’t standard notation. But writing ∆x -> 0 requires another step of thinking: y = f(x) therefore ∆y = ∆f(x) = f(x + ∆x) - f(x) so you only need ∆x approaching zero. But I prefer thinking d = lim (∆ -> 0) ∆.