FORMULARIO CÁLCULO DIFERENCIAL
Enviado por Miguel Itehua • 7 de Septiembre de 2021 • Apuntes • 640 Palabras (3 Páginas) • 141 Visitas
[pic 1] | FORMULARIO CÁLCULO DIFERENCIAL | [pic 2] |
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1. − 𝐷𝑥(𝐾) = 0 | 2. − 𝐷𝑥(𝑥𝑛) = 𝑛𝑥𝑛−1 | 3. −𝐷𝑥(𝑢𝑛) = 𝑛𝑢´𝑢𝑛−1 |
4. − 𝐷𝑥(𝑢𝑣) = 𝑢𝑣´ + 𝑣𝑢´ | 𝑢 𝑣𝑢´ − 𝑢𝑣´ 5. − 𝐷𝑥 (𝑣) = 𝑣2 | |
6. − 𝐷𝑥(𝑎𝑢) = 𝑢´𝑎𝑢𝑙𝑛𝑎 | 7. − 𝐷𝑥(𝑒𝑢) = 𝑢´𝑒𝑢 | 8. − 𝐷 (𝑢𝑣) = 𝑢𝑣 (𝑢´𝑣 + 𝑣´𝑙𝑢𝑢) 𝑥 𝑢 |
𝑢´𝑙𝑜𝑔𝑎𝑒 9. − 𝐷𝑥(𝑙𝑜𝑔𝑎𝑢) = 𝑢 | 𝑢´ 10. − 𝐷𝑥(𝑙𝑛𝑢) = 𝑢 | |
11. − 𝐷𝑥(𝑆𝑒𝑛𝑢) = 𝑢´𝐶𝑜𝑠𝑢 | 12. − 𝐷𝑥(𝐶𝑜𝑠𝑢) = −𝑢´𝑆𝑒𝑛𝑢 | 13. − 𝐷𝑥(𝑇𝑎𝑛𝑢) = 𝑢´𝑆𝑒𝑐2𝑢 |
14. − 𝐷𝑥(𝐶𝑜𝑡𝑎𝑛𝑢) = −𝑢´𝐶𝑠𝑐2𝑢 | 15. − 𝐷𝑥(𝑆𝑒𝑐𝑢) = 𝑢´𝑆𝑒𝑐𝑢𝑇𝑎𝑛𝑢 | 16. − 𝐷𝑥(𝐶𝑠𝑐𝑢) = −𝑢𝐶𝑠𝑐𝑢´𝐶𝑜𝑡𝑎𝑛𝑢 |
𝑢´ 17. − 𝐷𝑥(𝐴𝑟𝑐𝑆𝑒𝑛𝑢) = √1 − 𝑢2 | 𝑢´ 18. − 𝐷𝑥(𝐴𝑟𝑐𝐶𝑜𝑠𝑢) = − √1 − 𝑢2 | 𝑢´ 19. − 𝐷𝑥(𝐴𝑟𝑐𝑇𝑎𝑛𝑢) = 1 + 𝑢2 |
𝑢´ 20. − 𝐷𝑥(𝐴𝑟𝑐𝐶𝑜𝑡𝑎𝑛𝑢) = − 𝑢2 + 1 | 𝑢´ 21. − 𝐷𝑥(𝐴𝑟𝑐𝑆𝑒𝑐𝑢) = 𝑢√𝑢2 − 1 | 𝑢´ 22. − 𝐷𝑥𝐴𝑟𝑐𝐶𝑠𝑐𝑢 = − 𝑢√𝑢2 − 1 |
[pic 13] | FORMULARIO CÁLCULO INTEGRAL | [pic 14] |
1. − ∫ 𝑑𝑢 = 𝑢 + 𝑐 | 𝑥𝑛+1 2. − ∫ 𝑥𝑛𝑑𝑥 = + 𝑐 𝑛 + 1 | 𝑢𝑛+1 3. − ∫ 𝑢𝑛𝑑𝑢 = + 𝑐 𝑛 + 1 |
𝑑𝑢 4. − ∫ = 𝑙𝑛𝑢 + 𝑐 𝑢 | 5. − ∫ 𝑒𝑢𝑑𝑢 = 𝑒𝑢 + 𝑐 | 𝑎𝑢 6. − ∫ 𝑎𝑢𝑑𝑢 = + 𝑐 𝑙𝑛𝑎 |
7. − ∫ 𝑆𝑒𝑛𝑢𝑑𝑢 = −𝐶𝑜𝑠𝑢 + 𝑐 | 8. − ∫ 𝐶𝑜𝑠𝑢𝑑𝑢 = 𝑆𝑒𝑛𝑢 + 𝑐 | 9. − ∫ 𝑡𝑎𝑛𝑢𝑑𝑢 = 𝑙𝑛|𝑆𝑒𝑐𝑢| + 𝑐 |
10. − ∫ 𝐶𝑜𝑡𝑎𝑛𝑢𝑑𝑢 = 𝑙𝑛|𝑆𝑒𝑛𝑢| + 𝑐 | 11. ∫ 𝑆𝑒𝑐𝑢𝑑𝑢 = 𝑙𝑛|𝑆𝑒𝑐𝑢 + 𝑡𝑎𝑛𝑢| + 𝑐 | 12. ∫ 𝐶𝑠𝑐𝑢𝑑𝑢 = 𝑙𝑛|𝐶𝑠𝑐𝑢 + 𝐶𝑜𝑡𝑎𝑛𝑢| + 𝑐 |
13. ∫ 𝑆𝑒𝑐2𝑢𝑑𝑢 = 𝑇𝑎𝑛𝑢 + 𝑐 | 14. ∫ 𝐶𝑠𝑐2𝑢𝑑𝑢 = −𝐶𝑜𝑡𝑎𝑛𝑢 + 𝑐 | 15. ∫ 𝑆𝑒𝑐𝑢𝑇𝑎𝑛𝑢𝑑𝑢 = 𝑆𝑒𝑐𝑢 + 𝑐 |
16. ∫ 𝐶𝑠𝑐𝑢𝐶𝑜𝑡𝑎𝑛𝑢𝑑𝑢 = −𝐶𝑠𝑐𝑢 + 𝑐 | 𝑑𝑢 𝑢 17. ∫ = 𝐴𝑟𝑐𝑆𝑒𝑛 ( ) + 𝑐 √𝑎2 − 𝑢2 𝑎 | 𝑑𝑢 1 𝑢 18. ∫ = 𝐴𝑟𝑐𝑇𝑎𝑛 ( ) + 𝑐 𝑢2 + 𝑎2 𝑎 𝑎 |
𝑑𝑢 1 𝑢 − 𝑎 19. ∫ 𝑢2 − 𝑎2 = 2𝑎 𝑙𝑛 ( + 𝑎) + 𝑐 𝑢 | 𝑑𝑢 1 𝑢 + 𝑎 20. ∫ 𝑎2 − 𝑢2 = 2𝑎 𝑙𝑛 ( − 𝑎) + 𝑐 𝑢 | 𝑑𝑢 21. ∫ = 𝑙𝑛 (𝑢 + √𝑢2 ± 𝑎2) + 𝑐 √𝑢2 ± 𝑎2 |
𝑢 22. ∫ √𝑎2 − 𝑢2𝑑𝑢 = √𝑎2 − 𝑢2 2 𝑎2 𝑢 + 𝐴𝑟𝑐𝑆𝑒𝑛 ( ) + 𝑐 2 𝑎 | [pic 15] 23. ∫ √𝑢2 ± 𝑎2𝑑𝑢 𝑢 = √𝑢2 ± 𝑎2 𝑎 𝑎2 ± 𝑙𝑛 (𝑢 + √𝑢2 ± 𝑎2) + 𝑐 2 | 𝑑𝑢 1 𝑢 24. ∫ = 𝐴𝑟𝑐𝑆𝑒𝑛 ( ) + 𝑐 𝑢√𝑢2 − 𝑢2 𝑎 𝑎 |
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