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Reference · stzMathFunction

DerivativeAt()

the partial derivative with respect to one named variable

Basic examples (2)

Softanza
oQ = new stzMathFunction("x^2 - 2", [ "x" ])
? oQ.DerivativeAt("x", [ 0 ])
? oQ.DerivativeAt("x", [ 1 ])
Output
0
2

run on 2026-10-02 04:25 inside the library at commit 0e72e2e2c; taken from 15-an-identity-is-not-a-self-check.en.md(opens in a new tab)

Softanza
oQ = new stzMathFunction("x^2 - 2", [ "x" ])
? oQ.DerivativeAt("x", [ 0 ])
? oQ.DerivativeAt("x", [ 1.41421356 ])
Output
0
2.83

run on 2026-10-02 04:25 inside the library at commit 0e72e2e2c; taken from 14-the-derivative-that-checks.en.md(opens in a new tab)

Scope (2)

Softanza
oS = new stzMathFunction("sin(x)", [ "x" ])
? oS.DerivativeAt("x", [ 0 ])
? fabs( oS.DerivativeAt("x", [ 0 ]) - cos(0) ) < 0.000000001
Output
1
1

run on 2026-10-02 04:25 inside the library at commit 0e72e2e2c; taken from 14-the-derivative-that-checks.en.md(opens in a new tab)

Softanza
oF = new stzMathFunction("x*x + x*x", [ "x" ])
# f(3) = 18
? oF.ValueAt([3])
# f'(3) = 12, not 6
? oF.DerivativeAt("x", [3])
oG = new stzMathFunction("(x+y)*(x+y)", [ "x", "y" ])
# both operands of a shared node get their share
? oG.DerivativeAt("x", [2,3])
# ...and so does the other
? oG.DerivativeAt("y", [2,3])
Output
18
12
10
10

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_autodiff_narrated.ring(opens in a new tab)

The extensions of this method

Each extension, and whether it exists for this method; an extension that exists combines with the others (FindSTCS).

Extension
Exists
What it adds · The names
Q
no
does what the method does, then returns the object, so the call can be chained
QQ
no
chains on the next, more specific type of object (the Q ladder)
QQQ
no
chains on the most specific type of object (the Q ladder)
QRT
no
returns the result as an object of the requested type
CS
no
takes a case-sensitivity flag
ST
no
takes the position to start from (StartingAt)
IB
no
takes bounds that are included (IncludingBounds)
XT
no
the extended form: more parameters than the base method
XTT
no
yet another extension: a further extended form, after XT
Z
no
includes the position in what it returns
ZZ
no
returns positions as sections, [start, end]
W
no
selects by a condition
WF
no
selects by a condition, with the expressive keywords (@NextItem, @PreviousItem...)
D
no
takes a direction, forward or backward (Directional)
F
no
takes a function (the condition or the update is given as a function); the forms document also uses F for the future form, which defers the action
Many
no
works on a collection of items instead of one (the plural form)
Except
no
takes exceptions, what to leave out (the exceptional form)
U
no
returns the result without duplication

Every example is a test file of the library, run inside the library for this page; only those whose output kept every promise their file wrote are shown.

See also