this post was submitted on 14 Jul 2025
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I just think of the definition of a derivative.
d
is just an infinitesimally small delta. Sody/dx
is literally justlim (∆ -> 0) ∆y/∆x
. which is the same aslim (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 thinkingd = lim (∆ -> 0) ∆
.