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Rules of Derivatives: Table and Formulas, Study notes of Mathematics

Mathematics

The table and formulas for the rules of derivatives. It covers the derivatives of the sum, product, constant multiple, quotient, power, exponential, logarithmic, and trigonometric functions. The rules are presented in both algebraic and symbolic forms, along with examples for each rule.

Typology: Study notes

2020/2021

Uploaded on 04/07/2021

Mercury001
Mercury001 ๐Ÿ‡ฆ๐Ÿ‡ท

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Tabla de derivadas
Reglas de derivaciรณn
Sean ๐‘“ y ๐‘” funciones derivables
1) (๐‘“(๐‘ฅ)ยฑ ๐‘”(๐‘ฅ))โ€ฒ= ๐‘“โ€ฒ(๐‘ฅ)ยฑ ๐‘”โ€ฒ(๐‘ฅ)
2) (๐‘“(๐‘ฅ).๐‘”(๐‘ฅ))โ€ฒ= ๐‘“โ€ฒ(๐‘ฅ)๐‘”(๐‘ฅ)+ ๐‘“(๐‘ฅ) ๐‘”โ€ฒ(๐‘ฅ)
3) (๐‘˜ ๐‘”(๐‘ฅ))โ€ฒ= ๐‘˜ ๐‘”โ€ฒ(๐‘ฅ) (๐‘˜ โˆˆ โ„)
4) (๐‘“(๐‘ฅ)
๐‘”(๐‘ฅ))โ€ฒ= ๐‘“โ€ฒ(๐‘ฅ)๐‘”(๐‘ฅ)โˆ’๐‘“(๐‘ฅ) ๐‘”โ€ฒ(๐‘ฅ)
(๐‘”(๐‘ฅ))2
๐‘“(๐‘ฅ)
๐‘“ โ€ฒ(๐‘ฅ)
๐‘˜ (๐‘˜ โˆˆ โ„)
0
๐‘˜๐‘ฅ (๐‘˜ โˆˆ โ„)
๐‘˜
๐‘ฅ๐‘› (๐‘› โˆˆ โ„)
๐‘›๐‘ฅ๐‘›โˆ’1
๐‘’๐‘ฅ
๐‘’๐‘ฅ
๐‘Ž๐‘ฅ (๐‘Ž > 0 โˆง ๐‘Ž โ‰  1)
๐‘Ž๐‘ฅln๐‘Ž
๐‘ ๐‘’๐‘› ๐‘ฅ
cos๐‘ฅ
cos๐‘ฅ
โˆ’ ๐‘ ๐‘’๐‘› ๐‘ฅ
๐‘ก๐‘” ๐‘ฅ
1
๐‘๐‘œ๐‘ 2๐‘ฅ

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Tabla de derivadas

Reglas de derivaciรณn

Sean ๐‘“ y ๐‘” funciones derivables

โ€ฒ = ๐‘“โ€ฒ(๐‘ฅ) ยฑ ๐‘”โ€ฒ(๐‘ฅ)

โ€ฒ

โ€ฒ = ๐‘˜ ๐‘”โ€ฒ(๐‘ฅ) (๐‘˜ โˆˆ โ„)

๐‘“(๐‘ฅ) ๐‘”(๐‘ฅ)

โ€ฒ

๐‘“โ€ฒ(๐‘ฅ)๐‘”(๐‘ฅ)โˆ’๐‘“(๐‘ฅ) ๐‘”โ€ฒ(๐‘ฅ) (๐‘”(๐‘ฅ))^2

๐‘ฅ๐‘›^ (๐‘› โˆˆ โ„) ๐‘›๐‘ฅ๐‘›โˆ’^1

๐‘’๐‘ฅ^ ๐‘’๐‘ฅ

๐‘Ž๐‘ฅ^ (๐‘Ž > 0 โˆง ๐‘Ž โ‰  1 ) (^) ๐‘Ž๐‘ฅ^ ln ๐‘Ž ๐‘ ๐‘’๐‘› ๐‘ฅ cos ๐‘ฅ cos ๐‘ฅ โˆ’ ๐‘ ๐‘’๐‘› ๐‘ฅ ๐‘ก๐‘” ๐‘ฅ 1 ๐‘๐‘œ๐‘ ^2 ๐‘ฅ