Fungrim entry: 452407

Symbol: RealDerivative $\frac{d}{d x}\, f\!\left(x\right)$ Real derivative
The call syntax for this operator is the same as for Derivative.
The result is defined as $f'(x) = \lim_{h \to 0} \frac{f\!\left(x + h\right) - f(x)}{h}$ where the limit is taken with respect to a real variable $h$ ( RealLimit ).
Note that $x$ can be complex and that the "real derivative" can be complex-valued; the "real" qualifier just refers to the direction in which the limit is computed.
Definitions:
Fungrim symbol Notation Short description
RealDerivative$\frac{d}{d x}\, f\!\left(x\right)$ Real derivative
Derivative$\frac{d}{d z}\, f\!\left(z\right)$ Derivative
RealLimit$\lim_{x \to a} f(x)$ Limiting value, real variable
Source code for this entry:
Entry(ID("452407"),
SymbolDefinition(RealDerivative, RealDerivative(Call(f, x), For(x, x)), "Real derivative"),
Description("The call syntax for this operator is the same as for", SourceForm(Derivative), "."),
Description("The result is defined as", Equal(RealDerivative(f(x), For(x, x)), RealLimit(Div(Sub(f(Add(x, h)), f(x)), h), For(h, 0))), "where the limit is taken with respect to a real variable", h, "(", SourceForm(RealLimit), ")."),
Description("Note that", x, "can be complex and that the \"real derivative\" can be complex-valued; the \"real\" qualifier just refers to the direction in which the limit is computed."))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC