Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics

n

� The roots of the equation z � rcis� are

� � 2 � � cis , k �0,1 , 2 , , n�

1 n

1 k z r ⁿ

� De Moivre ’ s theorem : If n n z� rcis�

, then z � r cisn�

� Derivatives of a function y � f ( x)

:

1 .

2 .

3 . dy � f�( x)

: First derivative dx

2 d y d �d �

2 � d d d

y� �� f��( x)

: Second derivative x x � x � n d y n dx

( n)

� : n -th derivative f

( x)

� Rules of differentiation :

n n 1

� � � � ( ) ( ) ( ) ( ) ( ) ( ) f ( x) x f ( x) nx ^� f x � p x � q x � f � x � p� x � q� x

f ( x) � e ^x � f �( x)

� e 1 f ( x) � ln x � f �( x)

� x

x px ( ) f( x)

� qx ( ) p�( x) q( x) � p( x) q�( x)

� f�( x) �

2

( qx ( ))

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