this post was submitted on 14 Jul 2025
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I think rather
d/dxis the operator. You apply it to an expression to bind free occurrences ofxin that expression. For example,dx²/dxis best understood asd/dx (x²). The notation would be clear if you implement calculus in a program.If not fraction, why fraction shaped?
I just think of the definition of a derivative.
dis just an infinitesimally small delta. Sody/dxis 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:
∆ -> 0isn't standard notation. But writing∆x -> 0requires another step of thinking:y = f(x)therefore∆y = ∆f(x) = f(x + ∆x) - f(x)so you only need∆xapproaching zero. But I prefer thinkingd = lim (∆ -> 0) ∆.