Fungrim entry: 1b6a57

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 entry

Operators