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Ejercicios TEMA-3 DERIVADAS 2ºBACH

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Ejercicios del tema 3 del currículum de 2ºBACH, completos y variados. Problemas de distintos niveles de derivadas con posibles ejercicios de examen, que son ideales para preparar tu siguiente examen o reforzar tus conocimientos. Se complementan con su explicación teórica, disponible también en mi perfil. Perfectos para preparar la selectividad.

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EJERCICIOS DE DERIVADAS

𝑥 2 −3 25. 𝑓(𝑥) = 𝑙𝑛(2𝑥 − 1)
1. 𝑓(𝑥) =
𝑥 2 +3
𝑥2
3 26. 𝑓(𝑥) = 𝑡𝑔 ( )
2. 𝑓(𝑥) = √3𝑥 2 2

1−𝑥
2⁄
3 27. 𝑓(𝑥) = 𝑙𝑛(𝑥 2 − 1)
3. 𝑓(𝑥) = ( )
1+𝑥
28. 𝑓(𝑥) = 𝑎𝑟𝑐𝑐𝑜𝑠(√2𝑥)
2 𝑥2
4. 𝑓(𝑥) = +
𝑥 2 29. 𝑓(𝑥) = 𝑙𝑛(√1 − 𝑥)
ln(𝑥) 2
5. 𝑓(𝑥) = 30. 𝑓(𝑥) = (𝑎𝑟𝑐𝑡𝑔(𝑥))
𝑥

6. 𝑓(𝑥) = 7𝑒 −𝑥 31. 𝑓(𝑥) = 𝑙𝑜𝑔3 (7𝑥 + 2)
𝑒 𝑥 +𝑒 −𝑥 3
7. 𝑓(𝑥) = 32. 𝑓(𝑥) = 𝑙𝑛 [𝑡𝑔 ( )]
𝑒 𝑥 −𝑒 −𝑥 𝑥

8. 𝑓(𝑥) = 𝑠𝑒𝑛(𝑥) · 𝑐𝑜𝑠(𝑥) 33. 𝑓(𝑥) = 𝑒 4𝑥
1 1
9. 𝑓(𝑥) = 34. 𝑓(𝑥) = 𝑙𝑛 [𝑙𝑛 ( )]
𝑠𝑒𝑛(𝑥) 𝑥

10. 𝑓(𝑥) = 𝑙𝑛(𝑥 2 + 1) 35. 𝑓(𝑥) = 25𝑥
𝑥 𝑥+1
11. 𝑓(𝑥) = 𝑎𝑟𝑐𝑡𝑔 ( ) 36. 𝑓(𝑥) = 𝑎𝑟𝑐𝑠𝑒𝑛 ( )
3 𝑥−1

12. 𝑓(𝑥) = 𝑐𝑜𝑠 2 (2𝑥 − 𝜋) 37. 𝑓(𝑥) = 5 · 𝑡𝑔3 (3𝑥 2 + 1)
13. 𝑓(𝑥) = 𝑠𝑒𝑛2 (𝑥) 38. 𝑓(𝑥) = √𝑥 + √𝑥
14. 𝑓(𝑥) = 𝑠𝑒𝑛(𝑥 2 )
39. 𝑓(𝑥) = √𝑡𝑔(𝑥 2 )
15. 𝑓(𝑥) = √𝑡𝑔(𝑥)
3 𝑥−2
2 40. 𝑓(𝑥) = √
16. 𝑓(𝑥) = 𝑎𝑟𝑐𝑡𝑔(𝑥 + 1) 𝑥+2

7
17. 𝑓(𝑥) = (2√𝑥 − 3) 1−𝑥
41. 𝑓(𝑥) = 𝑙𝑛 (√ )
𝑥+1
18. 𝑓(𝑥) = 𝑙𝑜𝑔2 (√𝑥)
2
2 (𝑥 2 ) 42. 𝑓(𝑥) = 𝑙𝑛(𝑥 · 𝑡𝑔(𝑥))
19. 𝑓(𝑥) = 𝑠𝑒𝑛
3
1 √𝑥 2 −1
20. 𝑓(𝑥) = 𝑎𝑟𝑐𝑡𝑔 ( ) 43. 𝑓(𝑥) = 𝑙𝑛 ( )
𝑥 𝑥2

21. 𝑓(𝑥) = 𝑐𝑜𝑠 5 (7𝑥 2 ) 44. 𝑓(𝑥) = 𝑙𝑛(2𝑥 · 𝑠𝑒𝑛2 (𝑥))
22. 𝑓(𝑥) = 3𝑥 + 1 45. 𝑓(𝑥) = 𝑥 𝑒
𝑥


3
23. 𝑓(𝑥) = √(5𝑥 − 3)2 46. 𝑓(𝑥) = [𝑙𝑛(𝑥)]𝑥+1
𝑥2
24. 𝑓(𝑥) = 𝑎𝑟𝑐𝑠𝑒𝑛 ( )
3

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