Fungrim entry: 2a11ab

\frac{d}{d z}\, \sqrt{z} = \frac{1}{2 \sqrt{z}}

Assumptions:

z \in \mathbb{C} \setminus \left(-\infty, 0\right]

TeX:

\frac{d}{d z}\, \sqrt{z} = \frac{1}{2 \sqrt{z}}

z \in \mathbb{C} \setminus \left(-\infty, 0\right]

Definitions:

Fungrim symbol	Notation	Short description
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`Sqrt`	$\sqrt{z}$	Principal square root
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("2a11ab"),
    Formula(Equal(ComplexDerivative(Sqrt(z), For(z, z, 1)), Div(1, Mul(2, Sqrt(z))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))))

Topics using this entry

Square roots

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