Formulário-regras De Derivação
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Formulário-regras De Derivação as PDF for free.
More details
- Words: 373
- Pages: 1
DMCT, Universidade do Minho C´alculo A e B / An´alise Matem´atica I
2007/2008 MIEEIC, MIECOM. MIEMAT, MIEPOL, MIEMEC / LEC
Regras de deriva¸c˜ao Na lista de derivadas que se segue, omitem-se os dom´ınios das fun¸c˜oes.
1. C 0 = 0,
sendo C uma constante 0
2. (kf (x))0 = kf 0 (x)
(k ∈ R)
3. (f (x) + g(x)) = f 0 (x) + g 0 (x)
4. (f α (x))0 = αf α−1 (x)f 0 (x)
5. (f (x)g(x))0 = f 0 (x)g(x) + f (x)g 0 (x)
6.
7. (f ◦ g)0 (x) = f 0 (g(x)) g 0 (x)
8. (f −1 )0 (x) =
9. (ef (x) )0 = f 0 (x) ef (x)
10. (ln f (x))0 =
11. (af (x) )0 = f 0 (x) af (x) ln a
12. (loga f (x))0 =
f (x) g(x)
0 =
(α ∈ R)
f 0 (x)g(x) − f (x)g 0 (x) g 2 (x) 1 f 0 (f −1 (x)) f 0 (x) f (x) f 0 (x) loga e f (x)
13. ((f (x))g(x) )0 = g(x)(f (x))g(x)−1 f 0 (x) + g 0 (x)(f (x))g(x) ln f (x) 14. (senf (x))0 = f 0 (x) cosf (x) 16. (tgf (x))0 =
f 0 (x) cos2 f (x)
18. (shf (x))0 = f 0 (x) chf (x) 20. (thf (x))0 =
f 0 (x) ch2 f (x)
22. (arcsenf (x))0 = p 24. (arctgf (x))0 =
1 − f 2 (x)
f 0 (x) 1 + f 2 (x)
26. (argshf (x))0 = p 28. (argthf (x))0 =
f 0 (x)
f 0 (x) 1 + f 2 (x)
f 0 (x) 1 − f 2 (x)
15. (cosf (x))0 = −f 0 (x) senf (x) 17. (cotgf (x))0 =
−f 0 (x) sen2 f (x)
19. (chf (x))0 = f 0 (x) shf (x) 21. (cothf (x))0 =
−f 0 (x) sh2 f (x)
−f 0 (x) 23. (arccosf (x))0 = p 1 − f 2 (x) 25. (arccotgf (x))0 =
−f 0 (x) 1 + f 2 (x)
27. (argchf (x))0 = p 29. (argcothf (x))0 =
f 0 (x) f 2 (x) − 1
f 0 (x) 1 − f 2 (x)
2007/2008 MIEEIC, MIECOM. MIEMAT, MIEPOL, MIEMEC / LEC
Regras de deriva¸c˜ao Na lista de derivadas que se segue, omitem-se os dom´ınios das fun¸c˜oes.
1. C 0 = 0,
sendo C uma constante 0
2. (kf (x))0 = kf 0 (x)
(k ∈ R)
3. (f (x) + g(x)) = f 0 (x) + g 0 (x)
4. (f α (x))0 = αf α−1 (x)f 0 (x)
5. (f (x)g(x))0 = f 0 (x)g(x) + f (x)g 0 (x)
6.
7. (f ◦ g)0 (x) = f 0 (g(x)) g 0 (x)
8. (f −1 )0 (x) =
9. (ef (x) )0 = f 0 (x) ef (x)
10. (ln f (x))0 =
11. (af (x) )0 = f 0 (x) af (x) ln a
12. (loga f (x))0 =
f (x) g(x)
0 =
(α ∈ R)
f 0 (x)g(x) − f (x)g 0 (x) g 2 (x) 1 f 0 (f −1 (x)) f 0 (x) f (x) f 0 (x) loga e f (x)
13. ((f (x))g(x) )0 = g(x)(f (x))g(x)−1 f 0 (x) + g 0 (x)(f (x))g(x) ln f (x) 14. (senf (x))0 = f 0 (x) cosf (x) 16. (tgf (x))0 =
f 0 (x) cos2 f (x)
18. (shf (x))0 = f 0 (x) chf (x) 20. (thf (x))0 =
f 0 (x) ch2 f (x)
22. (arcsenf (x))0 = p 24. (arctgf (x))0 =
1 − f 2 (x)
f 0 (x) 1 + f 2 (x)
26. (argshf (x))0 = p 28. (argthf (x))0 =
f 0 (x)
f 0 (x) 1 + f 2 (x)
f 0 (x) 1 − f 2 (x)
15. (cosf (x))0 = −f 0 (x) senf (x) 17. (cotgf (x))0 =
−f 0 (x) sen2 f (x)
19. (chf (x))0 = f 0 (x) shf (x) 21. (cothf (x))0 =
−f 0 (x) sh2 f (x)
−f 0 (x) 23. (arccosf (x))0 = p 1 − f 2 (x) 25. (arccotgf (x))0 =
−f 0 (x) 1 + f 2 (x)
27. (argchf (x))0 = p 29. (argcothf (x))0 =
f 0 (x) f 2 (x) − 1
f 0 (x) 1 − f 2 (x)
Related Documents
De
November 2019 92
De
November 2019 101
De
May 2020 87
De
June 2020 79
De
June 2020 68
De
July 2020 56More Documents from "Patrick Johnston"
