Источник / закреплённая редакция
Defining the Derivative
Источник пакета openstax.calculus_derivatives · OpenStax Calculus, ch. 3 Derivatives, module m53495
- work
- urn:openstax:clir:calculus-derivatives#M53495
- номер
- OpenStax Calculus, ch. 3 Derivatives, module m53495
- вид
- urn:openstax:clir:calculus-derivatives#treatise
m53495/index.cnxml at commit 8dbc2ce (main, 2026-07-15)
- edition
- urn:openstax:clir:calculus-derivatives#M53495_MAIN
- язык
- en
- официальность
- official
- материализация
- PINNED_OFFICIAL_BYTES
- жизненный цикл
- adopted: 2026-07-15
Публикации
| URI | Тип | documentHash | Получено |
|---|---|---|---|
| https://raw.githubusercontent.com/openstax/osbooks-calculus-bundle/8dbc2ce19e804924b2517b89ac72ee45be949d15/modules/m53495/index.cnxml | application/xml; charset=utf-8 | sha256:d0668acbea9b24dfe647e4383e48b1b21c630f21b503883ef1e94eaa7406a4bf | 2026-09-12T00:00:00Z |
Фрагменты — 1
module/m53495#fs-id1169739095772 · defn · на него ссылаются: 7
en · official · sha256:4f9fa84e30bebdb099e77c49ef63f0c57168f36e082e3297e956386135f3e63aEN
<note id="fs-id1169739095772">
<title>Definition</title>
<para id="fs-id1169738924962">Let <m:math><m:mi>f</m:mi></m:math> be a function defined on an interval <m:math><m:mi>I</m:mi></m:math> containing <m:math><m:mi>a</m:mi><m:mo>.</m:mo></m:math> If <m:math><m:mrow><m:mi>x</m:mi><m:mo>≠</m:mo><m:mi>a</m:mi></m:mrow></m:math> is in <m:math><m:mi>I</m:mi><m:mo>,</m:mo></m:math> then</para>
<equation id="fs-id1169738850293"><m:math><m:mrow><m:mi>Q</m:mi><m:mo>=</m:mo><m:mfrac><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow><m:mo>−</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>a</m:mi><m:mo stretchy="false">)</m:mo></m:mrow><m:mrow><m:mi>x</m:mi><m:mo>−</m:mo><m:mi>a</m:mi></m:mrow></m:mfrac></m:mrow></m:math></equation>
<para id="fs-id1169738879993">is a <term id="term-00003">difference quotient</term>.</para>
<para id="fs-id1169739195558">Also, if <m:math><m:mrow><m:mi>h</m:mi><m:mo>≠</m:mo><m:mn>0</m:mn></m:mrow></m:math> is chosen so that <m:math><m:mrow><m:mi>a</m:mi><m:mo>+</m:mo><m:mi>h</m:mi></m:mrow></m:math> is in <m:math><m:mrow><m:mi>I</m:mi><m:mo>,</m:mo></m:mrow></m:math> then</para>
<equation id="fs-id1169739097936"><m:math><m:mrow><m:mi>Q</m:mi><m:mo>=</m:mo><m:mfrac><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mi>a</m:mi><m:mo>+</m:mo><m:mi>h</m:mi></m:mrow><m:mo>)</m:mo></m:mrow><m:mo>−</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>a</m:mi><m:mo stretchy="false">)</m:mo></m:mrow><m:mi>h</m:mi></m:mfrac></m:mrow></m:math></equation>
<para id="fs-id1169738913121">is a difference quotient with increment <m:math><m:mi>h</m:mi><m:mo>.</m:mo></m:math></para>
</note>Ссылаются нормы: DifferentiationRule, InstructionAvailable, instruction_available, rule_conclusion, rule_method, rule_premise, step_justified_by
Хэш рядом с текстом — sha256 его точных байтов. Он и есть проверка того, что показанный текст совпадает с закреплённым в пакете: расхождение роняет статику оракула.