Fungrim symbol: Derivative

Symbol: Derivative —

\frac{d}{d z}\, f\!\left(z\right)

— Derivative

This operator can be called with three or four arguments.

Derivative(f(z), z, a), rendered as

\left[ \frac{d}{d z}\, f\!\left(z\right) \right]_{z = a}

f'(a)

, represents the derivative of

f\!\left(z\right)

evaluated at

z = a

Derivative(f(z), z, a, n), rendered as

\left[ \frac{d^{n}}{{d z}^{n}} f\!\left(z\right) \right]_{z = a}

{f}^{(n)}(a)

, represents the order

n

derivative of

f\!\left(z\right)

evaluated at

z = a

The second argument

z

defines a locally bound variable for the expression in the first argument. With the evaluation point set to

a = z

, Derivative(f(z), z, z) may render more simply as

\frac{d}{d z}\, f\!\left(z\right)

This operator is ambiguous since the intended meaning could be a real derivative, a complex derivative, or some other form of derivative. It is better to use RealDerivative, ComplexDerivative, ComplexBranchDerivative, or MeromorphicDerivative.

Definitions:

Fungrim symbol	Notation	Short description
`Derivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Derivative
`RealDerivative`	$\frac{d}{d x}\, f\!\left(x\right)$	Real derivative
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`ComplexBranchDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative, allowing branch cuts
`MeromorphicDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative, allowing poles

Source code for this entry:

Entry(ID("1b6a57"),
    SymbolDefinition(Derivative, Derivative(Call(f, z), z, z), "Derivative"),
    Description("This operator can be called with three or four arguments."),
    Description(SourceForm(Derivative(f(z), z, a)), ", rendered as ", Derivative(Call(f, z), z, a), "or", Derivative(f(z), z, a), ", represents the derivative of", f(z), "evaluated at", Equal(z, a), "."),
    Description(SourceForm(Derivative(f(z), z, a, n)), ", rendered as ", Derivative(Call(f, z), z, a, n), "or", Derivative(f(z), z, a, n), ", represents the order", n, "derivative of", f(z), "evaluated at", Equal(z, a), "."),
    Description("The second argument", z, "defines a locally bound variable for the expression in the first argument. With the evaluation point set to", Equal(a, z), ",", SourceForm(Derivative(f(z), z, z)), "may render more simply as", Derivative(Call(f, z), z, z), "."),
    Description("This operator is ambiguous since the intended meaning could be a real derivative, a complex derivative, or some other form of derivative.", "It is better to use", SourceForm(RealDerivative), ",", SourceForm(ComplexDerivative), ",", SourceForm(ComplexBranchDerivative), ", or", SourceForm(MeromorphicDerivative), "."))

Topics using this symbol

The symbol Derivative appears in 18 topics:

Legendre polynomials (in 9 entries)
Sine (in 8 entries)
Inverse tangent (in 7 entries)
Coulomb wave functions (in 7 entries)
Operators (in 5 entries)
General analytic functions (in 5 entries)
Weierstrass elliptic functions (in 4 entries)
Airy functions (in 4 entries)
Square roots (in 3 entries)
Gauss hypergeometric function (in 2 entries)
Exponential function (in 2 entries)
Error functions (in 2 entries)
Confluent hypergeometric functions (in 2 entries)
Chebyshev polynomials (in 2 entries)
Gaussian quadrature (in 1 entries)
Euler's constant (in 1 entries)
Bounds and inequalities for the gamma function (in 1 entries)
Bernoulli numbers and polynomials (in 1 entries)

Entries using this symbol

The symbol Derivative appears in 65 entries: