DERIVATIVES AND INTEGRALS -...
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Basic Differentiation Rules Basic Integration Formulas DERIVATIVES AND INTEGRALS © Houghton Mifflin Company, Inc. 1. 4. 7. 10. 13. 16. 19. 22. 25. 28. 31. 34. 2. 5. 8. 11. 14. 17. 20. 23. 26. 29. 32. 35. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. 33. 36. d dx csch 1 u u u 1 u 2 d dx tanh 1 u u 1 u 2 d dx csch u csch u coth uu d dx tanh u sech 2 uu d dx arccsc u u u u 2 1 d dx arctan u u 1 u 2 d dx csc u csc u cot uu d dx tan u sec 2 uu d dx a u ln aa u u d dx ln u u u d dx u n nu n 1 u d dx uv uv vu d dx sech 1 u u u1 u 2 d dx cosh 1 u u u 2 1 d dx sech u sech u tanh uu d dx cosh u sinh uu d dx arcsec u u u u 2 1 d dx arccos u u 1 u 2 d dx sec u sec u tan uu d dx cos u sin uu d dx log a u u ln au u 0 d dx u u u u , d dx c 0 d dx u ± v u ± v d dx coth 1 u u 1 u 2 d dx sinh 1 u u u 2 1 d dx coth u csch 2 uu d dx sinh u cosh uu d dx arccot u u 1 u 2 d dx arcsin u u 1 u 2 d dx cot u csc 2 uu d dx sin u cos uu d dx e u e u u d dx x 1 d dx u v vu uv v 2 d dx cu cu 1. 3. 5. 7. 9. 11. 13. 15. 17. 2. 4. 6. 8. 10. 12. 14. 16. 18. du uu 2 a 2 1 a arcsec u a C du a 2 u 2 arcsin u a C sec u tan u du sec u C sec 2 u du tan u C sec u du ln sec u tan u C tan u du ln cos u C sin u du cos u C a u du 1 ln a a u C f u ± gu du f u du ± gu du du a 2 u 2 1 a arctan u a C csc u cot u du csc u C csc 2 u du cot u C csc u du ln csc u cot u C cot u du ln sin u C cos u du sin u C e u du e u C du u C kf u du k f u du
Transcript of DERIVATIVES AND INTEGRALS -...
Basic Differentiation Rules
Basic Integration Formulas
DERIVATIVES AND INTEGRALS
© Houghton Mifflin Company, Inc.
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4.
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16.
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31.
34.
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36.ddx
�csch�1 u� ��u�
�u��1 � u2
ddx
�tanh�1 u� �u�
1 � u2
ddx
�csch u� � ��csch u coth u�u�
ddx
�tanh u� � �sech2 u�u�
ddx
�arccsc u� ��u�
�u��u2 � 1
ddx
�arctan u� �u�
1 � u2
ddx
�csc u� � ��csc u cot u�u�
ddx
�tan u� � �sec2 u�u�
ddx
�au� � �ln a�auu�
ddx
�ln u� �u�
u
ddx
�un� � nun�1u�
ddx
�uv� � uv� � vu�
ddx
�sech�1 u� ��u�
u�1 � u2
ddx
�cosh�1 u� �u�
�u2 � 1
ddx
�sech u� � ��sech u tanh u�u�
ddx
�cosh u� � �sinh u�u�
ddx
�arcsec u� �u�
�u��u2 � 1
ddx
�arccos u� ��u�
�1 � u2
ddx
�sec u� � �sec u tan u�u�
ddx
�cos u� � ��sin u�u�
d
dx�loga u� �
u�
�ln a�u
u � 0ddx
��u�� �u
�u� �u��,
ddx
�c� � 0
ddx
�u ± v� � u� ± v�
ddx
�coth�1 u� �u�
1 � u2
ddx
�sinh�1 u� �u�
�u2 � 1
ddx
�coth u� � ��csch2 u�u�
ddx
�sinh u� � �cosh u�u�
ddx
�arccot u� ��u�
1 � u2
ddx
�arcsin u� �u�
�1 � u2
ddx
�cot u� � ��csc2 u�u�
ddx
�sin u� � �cos u�u�
ddx
�eu� � euu�
ddx
�x� � 1
ddx�
uv� �
vu� � uv�
v2
ddx
�cu� � cu�
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13.
15.
17.
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12.
14.
16.
18. du
u�u2 � a2�
1a
arcsec �u�a
� C
du�a2 � u2
� arcsin ua
� C
sec u tan u du � sec u � C
sec2 u du � tan u � C
sec u du � ln�sec u � tan u� � C
tan u du � �ln�cos u� � C
sin u du � �cos u � C
au du � 1ln a�au � C
� f�u� ± g�u�� du � f �u� du ± g�u� du
dua2 � u2 �
1a
arctan ua
� C
csc u cot u du � �csc u � C
csc2 u du � �cot u � C
csc u du � �ln�csc u � cot u� � C
cot u du � ln�sin u� � C
cos u du � sin u � C
eu du � eu � C
du � u � C
kf�u� du � kf�u� du
