Esercizi di ricapitolazione sul calcolo delle derivate

Esercizi svolti sulle derivate di funzioni continue

  1. y=\frac {2x+3}{x^2-x}
  2. y=\frac {x^4}{x^3+1}
  3. y=\frac {x^2}{(x-1)^3}
  4. y=\frac {(2x+1)^3}{x^4}
  5. y=\frac {(x-1)^2}{(2x-1)^3}
  6. y=\frac {3}{\sqrt[3]{2+x^2}}
  7. y=\sqrt {\frac {x+2}{3x}}
  8. y=\frac {x-2}{\sqrt[4]{x-2}}
  9. y=(\frac {2x}{3a-x})^{\frac 32}
  10. y=\frac {\sqrt{2-x^2}}{x}
  11. y=\frac {cosx}{1+cos^2x}
  12. y=5^x +5^{cosx}
  13. y=logsen\sqrt{2x+1}
  14. y=arctgx + log(1+x^2)
  15. y=\frac {x}{\sqrt {1+x}}
  16. y=log(x^2-3x+1)^2
  17. y=\frac {2-3senx}{senx-cosx}
  18. y=log_3(1+sen^2x)
  19. y=log_a(x^2+3)
  20. y=log|x^2-1| + log(x^2+1)
  21. y=\frac {2x+4}{\sqrt {x+1}}
  22. y=log_x5 (ricordare la formula del cambiamento di base)
  23. y=log \frac {1-x}{1+x}-2log(1-x^2)
  24. y=log_3x+\frac {2}{log_x3}
  25. y=sen2\sqrt x +2\sqrt {senx}
  26. y=(senx+x)(x-senx)
  27. y=log cos senx^3
  28. y=log \sqrt {arctg 2x}
  29. y=x \cdot arctg \frac 1x
  30. y= arct (-cotgx)
  31. y=logx-arctglogx
  32. y=arctg \frac {2x}{1-x^2}
  33. y=xlog_2x
  34. y=e^x\left [x^2-2(x-1)\right ]
  35. y=\sqrt[5]{sen^3x}
  36. y=arcsen \frac {x}{\sqrt {x^2+1}}
  37. y=sen^2x \cdot cos2x
  38. y=\frac {1+tg^2x}{1+cotg^2x}
  39. y=arctg \frac {1}{\sqrt {x^2-1}}+ \sqrt {x^2-1}
  40. y=tg e^{x^2+3}
  41. y=(x+2)^{logx}
  42. y=log(2senx + sen2x)^2
  43. y= arctg \sqrt {x^2-1}
  44. y=arcsen \frac xa \mbox{ , con } a>0
  45. y=arccos \frac { 1}{\sqrt {1+x^2}}
  46. y=arcsenx - \sqrt {1-x^2}
  47. y=log\left[3(x+\sqrt{9+x^2})\right]
  48. y=\frac {arcsenx}{arccosx}
  49. y=arcsen \sqrt {1-x^2}
  50. y=(sen \frac {\pi}{6})^{arctg \sqrt x}
  51. y=(tg \frac {\pi}{3})^2sen^22x
  52. y= \frac {x}{log_x2}
  53. y=log_{x^2}(2x+3)
  54. y=arccos(senx)
  55. y=arcsen(cosx)
  56. y=\frac {\sqrt{x+1}-\sqrt{x-1}}{\sqrt{x+1}+\sqrt{x-1}}
  57. y=logx^2+2\sqrt x
  58. y=senx^{x^2+1}
  59. y=(cos2x-cos^2x)^3
  60. y=x+sen2xcos2x
  61. y=7^{x^2}+x^{\sqrt 7}
  62. y=log \left[\pi (\sqrt 6+2)^2\right]
  63. y=e^{arctgx}+\sqrt {arctgx}
  64. y=2arctg \frac {1-cosx}{senx}
  65. y=\sqrt {\frac{1-cosx}{1+cosx}}
  66. y= \sqrt {\frac {sen^2x+tgx}{sen2x}}
  67. y=e^{-x}(x^3+\frac {x^4}{4})
  68. y=\frac {sen2x}{2senx (1+cos^2x)}
  69. y=\frac {sen^2x+tgx}{sen2x}
  70. y=\sqrt {\frac {1+senx}{1-senx}}
  71. y=arctg \frac {3x-x^3}{1-3x^2}
  72. y=2arctgx+ \frac {4x+1}{2x^2}
  73. y=log_{logx}x
  74. y=log_x(x+1)
  75. y=arctg \frac {senx}{1+cosx}
  76. y= 4logx +\frac {x^2-8x+1}{x-2}
  77. y= \frac {sen (x+30^\circ)}{sen(x-45^\circ)}
  78. y= \frac {cos (x+45^\circ)}{cos(75^\circ-x)}
  79. y=arctgx + arctg \frac {x^2-x}{1+x^3}
  80. y=arctg \frac {x+1}{1-x} + arctg \frac {x+\sqrt 3}{1-\sqrt 3x}+log \frac {1+x}{1-x}
  81. y= x^{\frac 1x}
  82. y=log |x| + \frac {1}{3x^3}
  83. y= log(2x +\sqrt {1+4x^2})
  84. y= 2x \sqrt {1+4x^2}+log(2x+\sqrt{1+4x^2})+4
  85. y=x(x+2)+2\left [ 1-log(x-2)^3 \right ]

 

 

 

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