Fungrim home page

Fungrim entry: 2a11ab

ddzz=12z\frac{d}{d z}\, \sqrt{z} = \frac{1}{2 \sqrt{z}}
Assumptions:zC(,0]z \in \mathbb{C} \setminus \left(-\infty, 0\right]
\frac{d}{d z}\, \sqrt{z} = \frac{1}{2 \sqrt{z}}

z \in \mathbb{C} \setminus \left(-\infty, 0\right]
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(ComplexDerivative(Sqrt(z), For(z, z, 1)), Div(1, Mul(2, Sqrt(z))))),
    Assumptions(Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))))

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