Derivative

The derivative operator: the function that is the $n$th derivative of $f$.

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Derivative(f, orders*)Adds a closed-form derivative table for the heads this package defines, keyed by head and by $\partial$-order vector, so Derivative(f, orders*) returns a function literal instead of compute-engine's inert symbolic form; any head not in the table still falls through to native behavior.

Typed signatures

Type	Package	Applies
(function, order: number*) -> function	analyticreplaces compute-engine	always
(function, order: number*) -> function	compute-engine	always

Domain: Compute engine

Examples

Basic #

$\frac{d}{dz}\ln\Gamma(z) = \psi(z)$, the same Digamma that D of LogGamma gives

live ↗

In$\mathrm{LogGamma}^{\prime}$Out$z↦\mathrm{Digamma}(z)$

Scope #

The order vector picks the partial: here $\partial_b B(a, b) = B(a, b)(\psi(b) - \psi(a + b))$

live ↗

In$\Beta^{(0, 1)}$Out$(a, b)↦(\mathrm{Digamma}(b)-\mathrm{Digamma}(a+b))\mathrm{B}(a, b)$

$\partial_a \zeta(s, a) = -s\,\zeta(s + 1, a)$

live ↗

In$\Zeta^{(0, 1)}$Out$(s, a)↦-(sζ(s+1, a))$

Properties #

A head compute-engine already differentiates keeps its own rule

live ↗

In$Γ^{\prime}$Out$x↦Γ(x)\mathrm{Digamma}(x)$

About

Examples	4
Checked against	Wolfram Language 4 agree
Crosswalk	FungrimFungrim entry ×120Wolfram Language

See also: D