TEOREMAS PARA EL CÁLCULO DE LÍMITES:
1. lim
𝑥→𝑎𝑘=𝑘 k es número real (una constante)
8. lim
𝑥→𝑎[𝑓(𝑥)]𝑛= [ lim
𝑥→𝑎𝑓(𝑥)]𝑛
2. lim
𝑥→𝑎𝑥= 𝑎
9. lim
𝑥→∞ 𝑘
𝑥𝑛= 0
3. lim
𝑥→𝑎𝑘𝑥=𝑘𝑎 k es número real (una constante)
10. lim
𝑢→𝜙𝑠𝑒𝑛 𝑢= 𝑠𝑒𝑛 𝜙
4. lim
𝑥→𝑎𝑥𝑛=𝑎𝑛
11. lim
𝑢→𝜙𝑐𝑜𝑠 𝑢= 𝑐𝑜𝑠 𝜙
5. lim
𝑥→𝑎[ 𝑓(𝑥)±𝑔(𝑥)]= lim
𝑥→𝑎𝑓(𝑥) ± lim
𝑥→𝑎𝑔(𝑥)
12. lim
𝑢→0𝑠𝑒𝑛 𝑢= 0
6. lim
𝑥→𝑎[ 𝑓(𝑥) ∙ 𝑔(𝑥)]= lim
𝑥→𝑎𝑓(𝑥) ∙ lim
𝑥→𝑎𝑔(𝑥)
13. lim
𝑢→0𝑐𝑜𝑠 𝑢= 1
7. lim
𝑥→𝑎 𝑓(𝑥)
𝑔(𝑥) = lim
𝑥→𝑎𝑓(𝑥)
lim
𝑥→𝑎𝑔(𝑥) 𝑔(𝑥) ≠ 0
14. lim
𝑢→0 𝑠𝑒𝑛 𝑢
𝑢= 1
TEOREMAS PARA EL CÁLCULO DE DERIVADAS:
1. 𝑑
𝑑𝑥 𝑘 = 0
14. 𝑑
𝑑𝑥 𝑠𝑒𝑐 𝑢= sec 𝑢 tan𝑢 𝑑
𝑑𝑥 𝑢
2. 𝑑
𝑑𝑥𝑥= 1
15. 𝑑
𝑑𝑥 𝑐𝑠𝑐 𝑢= − csc 𝑢 cot𝑢 𝑑
𝑑𝑥 𝑢
3. 𝑑
𝑑𝑥 𝑘𝑥= 𝑘
16. 𝑑
𝑑𝑥 𝑎𝑟𝑐 𝑠𝑒𝑛 𝑢 = 1
√1−𝑢2 𝑑
𝑑𝑥𝑢
4. 𝑑
𝑑𝑥 𝑥𝑛=𝑛𝑥𝑛−1
17. 𝑑
𝑑𝑥 𝑎𝑟𝑐 𝑐𝑜𝑠 𝑢 =− 1
√1−𝑢2 𝑑
𝑑𝑥𝑢
5. 𝑑
𝑑𝑥 [𝑓(𝑥)±𝑔(𝑥)]= 𝑑
𝑑𝑥𝑓(𝑥)±𝑑
𝑑𝑥 𝑔(𝑥)
18. 𝑑
𝑑𝑥 𝑎𝑟𝑐 𝑡𝑎𝑛 𝑢 = 1
1+𝑢2 𝑑
𝑑𝑥𝑢
6. 𝑑
𝑑𝑥 [𝑓(𝑥)∙𝑔(𝑥)]= 𝑓(𝑥)𝑑
𝑑𝑥𝑔(𝑥)+𝑔(𝑥)𝑑
𝑑𝑥 𝑓(𝑥)
19. 𝑑
𝑑𝑥 𝑎𝑟𝑐 𝑐𝑜𝑡 𝑢 =− 1
1+𝑢2 𝑑
𝑑𝑥𝑢
7. 𝑑
𝑑𝑥[[𝑓(𝑥)
𝑔(𝑥)] = 𝑔(𝑥) 𝑑
𝑑𝑥 𝑓(𝑥) − 𝑓(𝑥) 𝑑
𝑑𝑥 𝑔(𝑥)
[𝑔(𝑥)]2 𝑔(𝑥)≠0
20. 𝑑
𝑑𝑥 𝑎𝑟𝑐 𝑠𝑒𝑐 𝑢 = 1
𝑢√𝑢2−1 𝑑
𝑑𝑥𝑢
8. 𝑑
𝑑𝑥 [𝑓(𝑥)]𝑛= 𝑛 [𝑓(𝑥)]𝑛−1
21. 𝑑
𝑑𝑥 𝑎𝑟𝑐 𝑠𝑒𝑐 𝑢 =− 1
𝑢√𝑢2−1 𝑑
𝑑𝑥𝑢
9. 𝑑
𝑑𝑥𝑘 𝑓(𝑥)= 𝑘 𝑑
𝑑𝑥 𝑓(𝑥)
22. 𝑑
𝑑𝑥 𝑙𝑜𝑔𝑎𝑢 = 1
𝑢 𝑙𝑜𝑔𝑎 𝑒 𝑑
𝑑𝑥𝑢
10. 𝑑
𝑑𝑥 𝑠𝑒𝑛 𝑢= cos 𝑢 𝑑
𝑑𝑥 𝑢
23. 𝑑
𝑑𝑥𝑙𝑛𝑢 = 1
𝑢 𝑑
𝑑𝑥𝑢
11. 𝑑
𝑑𝑥 𝑐𝑜𝑠 𝑢= −𝑠𝑒𝑛 𝑢 𝑑
𝑑𝑥 𝑢
24. 𝑑
𝑑𝑥𝑎𝑢= 𝑎𝑢𝑙𝑛𝑎 𝑑
𝑑𝑥 𝑢
12. 𝑑
𝑑𝑥 𝑡𝑎𝑛 𝑢 = 𝑠𝑒𝑐2𝑢 𝑑
𝑑𝑥 𝑢
25. 𝑑
𝑑𝑥𝑒𝑢 𝑑
𝑑𝑥𝑢
13. 𝑑
𝑑𝑥 𝑐𝑜𝑡 𝑢= − 𝑐𝑠𝑐2𝑢 𝑑
𝑑𝑥 𝑢
