Derivadas

EJERCICIOS DE DERIVACIÓN

1. y=x5+5x4-10x2+6 | dydx=5x(x3+4x2-4) |

2. y= 12x2+4x | dydx=-1x3-2x32 |

3. y=3+4x-x212 | y´=2-xy |

4. y=1+x | y´=14x+xx |

5.y=x2+342x3-53 | y´=2xx2+332x3-52(17x3+27x-20) |

6. y=a-xa+x | y´=-2aa+x2 |

7. y=a2+x2x | dydx=-a2x2a2+x2 |

8. y=1-cx1+cx | dydx=-c1+cx1-c2x2 |

9. y=a23-x2332 | dydx=3yx |10. ht=2cost | h´t=-sintt |

11. fx=sin3x- 12 | f´x=-3cos3x2sin3x32 |

12. fx=tanx2+1 | f´x=xx2+1secx2+12 |

13. y=lnax+b | dydx=aax+b |

14. y= lnax+b2 | dydx=2aax+b |

15.y=lnx+1+x2 | dydx=11+x2 |

16. fx=x2lnx2 | f´x=2x1+2lnx |

17. y=enx | dydx=nenx |

18. y=10nx | dydx=n10nxln10 |

19. s=et | dsdt=et2t |

20. y=lnxx | dydx=1-lnxx2|

21. y=ex-e-xex+e-x | dydx=4ex+e-x2 |

22. fx=lnx2+1-xx2+1+x | f´x=-2x2+1 |

23. y=xx | y´=xx2+lnx2x |

24. y=x33x+a2x+b | dydx=y1x+13x+a-12x+b |

25. y=xn a+bxm |dydx=ynx+mba+bx |

26. y=eaxsinbx | y´=eaxasinbx+bcosbx |
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27. fθ=sinθ+acosθ-a | f´θ=cos2θ |

28. y=xsinx | dydx=xsinxsinxx+cosxlnx |

29. y=cosxx | y´=ylncosx-xtanx|

30. y=sinkx | d2ydx2=-k2sinkx |

31. y=arccosxa | y´=-1a2-x2 |

32. y=arcsinx | dydx=12x-x2 |

33. y=x2arccosx | dydx=2x arccosx-x21-x2 |

34. fu=ua2-u2+a2arcsinua |f´u=2a2-u2 |

35. fx=a2-x2+a arcsinxa | f´x=a-xa+x |

36. v=ua2-u2-arc sinua | dvdu=u2a2-u232 |

37. v=a arccos1-ua+2au-u2 | dvdu=2au-u2u |

38. φ=arc tana+r1-ar |dφdr=11+r2 |

39. y=arcsinxa+a2-x2x | dydx=- a2-x2x2 |

40. y=x2 arccos2x | dydx=2xarccos2x+1x2-4 |

41. y=lnex+1+e2x | dydx=ex1+e2x |

42. y=lnx+ax2+b2+ab arctanxb | dydx=a2+b2x+ax2+b2|

43. y=abxbxaxab | y´=ylnab-a-bx si x > 0 |

44. y=arctanex-lne2xe2x+1 | dydx=ex-1e2x+1 |

45. y=lnarc cos1x | dydx=12xx-1 arccos1x |...