Summary Mathematics

Mathematics, English - Grade 12
Weekly Cheat Sheet
By
Bongani Monyoko


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Differentiation: the process of getting the derivative of a
function, or rate of change e.g �� or ��
�� ��



Rules of differentiation:

 General rule for differentiation:

��
��
[�� ] = ���−1 , where n ∈ R and n≠ 0

 The derivative of a constant is equal to zero:

�
[�] = 0
��

 The derivative of a constant multiplied by a function is
equal to the constant multiplied by the derivative of the
function:
� �
[� × �(�)] = � [�(�)]
�� ��

 The derivative of a sum is equal to the sum of derivatives:

� � �
��
[�(�) + �(�)]=�� [�(�)] + �� [�(�)]

 The derivative of a difference is equal to the difference of
derivatives:

� � �
��
[�(�) − �(�)]=�� [�(�)] − �� [�(�)]