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This flashcard set covers advanced calculus topics at an intermediate level, focusing on derivatives, integration, and related rules. It delves into various rules for differentiation, including the chain rule, and provides examples of derivatives for functions like sin(x), cos(x), and x². The set also explores integration techniques such as substitution and parts, with practical examples like integrating sin(x²) and x/(x²+1). Additionally, it includes rules for logarithms and exponentiation. This flashcard set is ideal for students and professionals seeking to strengthen their calculus skills, offering a comprehensive overview of key concepts and their applications.
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11
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8
Sprache
Englisch
Kategorie
Mathematik
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Andere
Erstellt / Aktualisiert
24.08.2020 / 26.03.2025
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Lernkarten

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Integration rules 1

 

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https://www.mathsisfun.com/calculus/integration-rules.html

 

see also: https://www.mathsisfun.com/calculus/integration-introduction.html

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Integration rules 2

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https://www.mathsisfun.com/calculus/integration-rules.html

 

see also https://www.mathsisfun.com/calculus/integration-introduction.html

Explain the integration by parts and solve the examples below:

1) What is ∫x cos(x) dx

2) ∫ln(x)/x2 dx

3) ∫ln(x) dx 

4) ∫ex x dx

5) ∫ex sin(x) dx

https://www.mathsisfun.com/calculus/integration-by-parts.html

Explain Integration by Substitution and solve the examples below:

1) ∫cos(x2) 2x dx

2) ∫cos(x2) 6x dx

3) ∫x/(x2+1) dx

4) ∫(x+1)3 dx

5) ∫(5x+2)7 dx

https://www.mathsisfun.com/calculus/integration-by-substitution.html

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Derivative rules 1

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https://www.mathsisfun.com/calculus/derivatives-rules.html

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Derivative rules 2

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https://www.mathsisfun.com/calculus/derivatives-rules.html
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Derivatives: Chain rule

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Additional explanation of the composition of funcitons:

 

https://www.mathsisfun.com/sets/functions-composition.html

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Derivative examples:

1) what is the derivative of sin(x)

5) What is the derivative of x2+x3 ?

8) What is the derivative of cos(x)sin(x) ?

9) What is the derivative of cos(x)/x ?

 

11) What is ddxsin(x2) ?

12) What is ddxsin(x2) ?

13)

14)

15)

https://www.mathsisfun.com/calculus/derivatives-rules.html

Integration examples:

1) what is the integral of sin(x) ?

2) what is the integral of 1/x ?

3) What is ∫x3 dx ?

4) What is ∫√x dx ?

5) What is ∫√x dx ?

6) What is ∫6x2 dx ?

7) What is ∫cos x + x dx ?

8) What is ∫ew − 3 dw ?

9) What is ∫8z + 4z3 − 6z2 dz ?

Solutions

https://www.mathsisfun.com/calculus/integration-rules.html

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Explonentiation rules 1

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https://mathinsight.org/exponentiation_basic_rules#:~:text=If%20n%20is%20a%20positive,the%20exponent%20or%20the%20power.

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Rules for logarithms 1

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https://mathinsight.org/logarithm_basics

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