2017年2月7日火曜日

学習環境

解析入門 原書第3版 (S.ラング(著)、松坂 和夫(翻訳)、片山 孝次(翻訳)、岩波書店)の第2部(微分と基本的な関数)、第3章(微分係数、導関数)、6(合成微分律(合成関数の微分法))、1-40.を取り組んでみる。

1-40.


    1. f( u )= u 8 ,g( x )=x+1

    2. f( u )= u 1 2 ,g( x )=2x5

    3. f( u )= u 3 ,g( x )=sinx

    4. f( u )= u 5 ,g( x )=logx

    5. f( u )=sinu,g( x )=2x

    6. f( u )=logu,g( x )= x 2 +1

    7. f( u )= e u ,g( x )=cosx

    8. f( u )=logu,g( x )= e x +sinx

    9. f( u )=sinu,g( x )=logx+ 1 x

    10. f( u )= 1 2 u+1 sinu ,g( x )=2x

    11. f( u )= u 3 ,g( x )=2 x 2 +3

    12. f( u )=cosu,g( x )=sin5x

    13. f( u )=logu,g( x )=cos2x

    14. f( u )=sinu,g( x )= ( 2x+5 ) 2

    15. f( u )=sinu,g( x )=cos( x+1 )

    16. f( u )=sinu,g( x )= e x

    17. f( u )= 1 u 4 ,g( x )=3x1

    18. f( u )= 1 u 3 ,g( x )=4x

    19. f( u )= 1 u 2 ,g( x )=sin2x

    20. f( u )= 1 u 2 ,g( x )=cos2x

    21. f( u )= 1 sinu ,g( x )=3x

    22. f( u )= 1 1 2 u ,g( x )=2sinxcosx=sin2x

    23. f( u )=( u 2 +1 ) e u ,g( x )=x

    24. f( u )=( u 3 +2u )( sin3u ),g( x )=x

    25. f( u )= 1 u ,g( x )=sinx+cosx

    26. f( u )= sin2u e u ,g( x )=x

    27. f( u )= logu u 2 +3 ,g( x )=x

    28. f( u )= u+1 cos2u ,g( x )=x

    29. f( u )=( 2u3 )( e u +u ),g( x )=x

    30. f( u )=u,g( x )=( x 3 1 )( e 3x +5x )

    31. f( u )=u,g( x )= x 3 +1 x1

    32. f( u )=u,g( x )= x 2 1 2x+3

    33. f( u )=u,g( x )=( x 4 3 e x )( 2x+1 )

    34. f( u )=u,g( x )=( sin3x )( x 1 4 1 )

    35. f( u )=sinu,g( x )= x 2 +5x

    36. f( u )= e u ,g( x )=3 x 2 +8

    37. f( u )= 1 logu ,g( x )= x 4 +1

    38. f( u )= 1 logu ,g( x )= x 1 2 +2x

    39. f( u )=u,g( x )= 2x e x

    1. 8 ( x+1 ) 7

    2. 1 2 ( 2x5 ) 1 2 ·2

    3. 3 ( sinx ) 2 cosx

    4. 5 ( logx ) 4 1 x

    5. cos2x·2

    6. 1 x 2 +1 ·2x

    7. e cosx ( sinx )

    8. 1 e x +sinx ( e x +cosx )

    9. cos( logx+ 1 x )·( 1 x 1 x 2 )

    10. sin2x( x+1 )cos( 2x )2 sin 2 2x

    11. 3 ( 2 x 2 +3 ) 2 ·4x

    12. sin( sin5x )·cos5x·5

    13. 1 cos2x ( sin2x·2 )

    14. cos ( 2x+5 ) 2 ·2( 2x+5 )·2

    15. cos( cos( x+1 ) )·( sin( x+1 ) )

    16. cos e x · e x

    17. 4( 3x1 )·3 ( 3x1 ) 8

    18. 3 ( 4x ) 2 4 ( 4x ) 6

    19. 2sin2x·2 ( sin2x ) 4

    20. 2cos2x·2 ( cos2x ) 4

    21. cos3x·3 sin 2 3x

    22. cos 2 x sin 2 x

    23. 2x e x +( x 2 +1 ) e x

    24. ( 3 x 2 +2 )sin3x+( x 3 +2x )cos3x·3

    25. ( cosxsinx ) sinx+cosx

    26. cos2x·2 e x sin2x· e x e 2x

    27. 1 x ( x 2 +3 )logx·2x ( x 2 +3 ) 2

    28. cos2x( x+1 )( sin2x )2 cos 2 2x

    29. 2( e x +x )+( 2x3 )( e x +1 )

    30. 3 x 2 ( e 3x +5x )+( x 3 1 )( e 3x ·3+5 )

    31. 3 x 2 ( x1 )( x 3 +1 ) ( x1 ) 2

    32. 2x( 2x+3 )( x 2 1 )2 ( 2x+3 ) 2

    33. ( 4 3 x 1 3 e x )( 2x+1 )+( x 4 3 e x )2

    34. cos3x·3( x 1 4 1 )+sin3x· 1 4 x 3 4

    35. cos( x 2 +5x )·( 2x+5 )

    36. e 3 x 2 +8 ·6x

    37. 1 x 4 +1 ·4 x 3 ( log( x 4 +1 ) ) 2

    38. 1 x 1 2 +2x ·( 1 2 x 1 2 +2 ) ( log( x 1 2 +2x ) ) 2

    39. 2 e x 2x e x e 2x

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