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Derivadas Exercicios, Exercises of Mathematics

Mount Royal University Mathematics

exercicios de derivadas matematica 2

Typology: Exercises

2018/2019

Uploaded on 12/17/2019

beatriz-pulici 🇨🇦

4 documents

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11a Aula - Derivadas

Derivada de uma constante

𝑓(𝑥)= 𝑘 → 𝑓´(𝑥)=0

Derivada da potência

𝑓(𝑥)=𝑥𝑛 → 𝑓´(𝑥)=𝑛∙𝑥𝑛−1

Derivada do produto de uma constante por

uma função

[𝑘𝑓(𝑥)]´ =𝑘∙𝑓´(𝑥)

Derivada de uma soma

[𝑓(𝑥)+𝑔(𝑥)]´ =𝑓´(𝑥)+𝑔´(𝑥)

Derivada do produto

[𝑓(𝑥)∙𝑔(𝑥)]´= 𝑓´(𝑥)∙𝑔(𝑥) + 𝑓(𝑥)∙𝑔´(𝑥)

Derivada do quociente

[𝑓(𝑥)

𝑔(𝑥)]´= 𝑓´(𝑥)∙𝑔(𝑥)−𝑓(𝑥)∙𝑔´(𝑥)

[𝑔(𝑥)]2

Derivada de 𝑒𝑥

𝑓(𝑥)=𝑒𝑥 → 𝑓´(𝑥)=𝑒𝑥

Derivada de ln𝑥

𝑓(𝑥)=ln𝑥 → 𝑓´(𝑥)=1

𝑥 , 𝑥 > 0

Regra da Cadeia

𝑦= 𝑓(𝑔(𝑥)) → 𝑑𝑦

𝑑𝑥 =𝑑𝑦

𝑑𝑢∙𝑑𝑢

𝑑𝑥

Regra do Externo-Interno

𝑑𝑦

𝑑𝑥 =𝑓´(𝑔(𝑥))∙𝑔´(𝑥)

Proposições

𝑦= 𝑓(𝑥)𝑥 → 𝑦´ = 𝑛 ∙ 𝑓(𝑥)𝑛−1 ∙𝑓´(𝑥)

𝑦= √𝑓(𝑥) =𝑓(𝑥)1

2 → 𝑦´ = 1

2√𝑓(𝑥)∙𝑓´(𝑥)

𝑦= 𝑒𝑓(𝑥) → 𝑦´ = 𝑒𝑓(𝑥) ∙ 𝑓´(𝑥)

𝑦= ln𝑓(𝑥) → 𝑦´ = 𝑓´(𝑥)

𝑓(𝑥)

Derivadas Sucessivas

𝑓´(𝑥) → 𝑑𝑒𝑟𝑖𝑣𝑎𝑑𝑎 𝑝𝑟𝑖𝑚𝑒𝑖𝑟𝑎 (1𝑎 𝑜𝑟𝑑𝑒𝑚)

𝑓´´(𝑥) → 𝑑𝑒𝑟𝑖𝑣𝑎𝑑𝑎 𝑠𝑒𝑔𝑢𝑛𝑑𝑎 (2𝑎 𝑜𝑟𝑑𝑒𝑚)

𝑓´´´(𝑥) → 𝑑𝑒𝑟𝑖𝑣𝑎𝑑𝑎 𝑡𝑒𝑟𝑐𝑒𝑖𝑟𝑎 (3𝑎 𝑜𝑟𝑑𝑒𝑚)

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a

Aula - Derivadas

Derivada de uma constante 𝑓(𝑥) = 𝑘 → 𝑓´(𝑥) = 0

Derivada da potência 𝑓(𝑥) = 𝑥

𝑛

𝑛− 1

Derivada do produto de uma constante por

uma função

[

]

Derivada de uma soma [𝑓(𝑥) + 𝑔(𝑥)]´ = 𝑓´(𝑥) + 𝑔´(𝑥)

Derivada do produto [𝑓(𝑥) ∙ 𝑔(𝑥)]´ = 𝑓´(𝑥) ∙ 𝑔(𝑥) + 𝑓(𝑥) ∙ 𝑔´(𝑥)

Derivada do quociente

[

] ´ =

[𝑔(𝑥)]

2

Derivada de 𝑒

𝑥

Derivada de ln 𝑥

𝑓(𝑥) = ln 𝑥 → 𝑓´(𝑥) =

Regra da Cadeia

Regra do Externo-Interno

Proposições 𝑦 = 𝑓(𝑥)

𝑥

𝑛− 1

1

2 → 𝑦´ =