Basic Differentiation Rules

Basic Integration Formulas

DERIVATIVES AND INTEGRALS

© Houghton Mifflin Company, Inc.

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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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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