InTech-Fractional Derivatives Fractional Integrals and Fractional Differential Equations in Matlab
DERIVATIVES AND INTEGRALS -...
Transcript of DERIVATIVES AND INTEGRALS -...
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.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�
1.
3.
5.
7.
9.
11.
13.
15.
17.
2.
4.
6.
8.
10.
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