Prepare for your exams
Get points
Guidelines and tips
Sell on Docsity
Docsity AI

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Docsity AI

Log in Sign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

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

1 / 1

This page cannot be seen from the preview

Don't miss anything!

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)

Discover Exercises of Mathematics Mount Royal University

Partial preview of the text

Download Derivadas Exercicios and more Exercises Mathematics in PDF only on Docsity!

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´ =