Analysis and Approaches for IBDP Maths Ebook 2 | Page 132

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Chapter
10
Differentiation
SUMMARY POINTs
�
�
�
Differentiation by first principle:
f�( x) � lim
f x �h � f x
h �0
( ) ( )
h
Differentiation rules:
2
f ( x) � tan x � f ( x) � sec x
�
2
f ( x) � cot x � f ( x) � � cosec x
f ( x) � sec x � f �( x) � sec x tan x f ( x) � cosec x � f �( x) � � cosecx cot x
( ) x
x
f x � a � f �( x) � a ln a
1
f ( x) � arcsin x � f �( x)
�
1�
x
1
f ( x) � arctan x � f �( x)
�
2
1 � x
Implicit differentiation:
F d d
( x , y ) � G ( x , y ) � ( , ) ( , )
d
F x y �
x dx
G x y
2
1
f ( x) � log
a
x � f �( x)
�
xln
a
f ( x) � arccos x � f �( x)
� �
�
1
1�
x
2
Solutions of Chapter 10
122
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