Fungrim entry: 3e71f4

\frac{d^{2}}{{d z}^{2}} \sqrt{z} = -\frac{1}{4 {z}^{3 / 2}}

Assumptions:

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

TeX:

\frac{d^{2}}{{d z}^{2}} \sqrt{z} = -\frac{1}{4 {z}^{3 / 2}}

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

Definitions:

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

Source code for this entry:

Entry(ID("3e71f4"),
    Formula(Equal(Derivative(Sqrt(z), Tuple(z, z, 2)), Neg(Div(1, Mul(4, Pow(z, Div(3, 2))))))),
    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.

2019-06-18 07:49:59.356594 UTC