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Fórmulas de Derivadas 
 
�) � = � �� = � �	) � = 
�� 
 �� = 
�� 
 . �� 
 ��) � = 
��� � �� = ��. ��
� � 
�) � = �. 
 �� = � ��) � = ��
�� 
 �� = −��
�� 
 . ���� 
 ��)� = ��
� � �� = ��. 
��� � 
�) � = �
� �� = �. �. 
��� ��) � = 
��� 
= �� ��
 − ��
) �� = ��
� 
 =
�� ��
 + ��
) ��) � = ��� � �� = ��. 
���� � 
�) � = � + � + �� = �� + �� + � �!) � = ��
� 
= �� ��
 + ��
) �� = 
��� 
 =
�� ��
 − ��
) ��) � = ����� � �� = ��. ��
���� � 
") � = � − � − �� = �� − �� − � ��) � = ��� 
= �
 − ��
�
 + ��
 �� = 
���� 
 =
���
 + ��
)� �") � = 
��� � �� = ��. 
��� � . ��� � 
	) � = �. � �� = �. �� + �. �′ ��) � = ����� 
= �
 + ��
�
 − ��
 
�� = −��
���� 
= − ���
 − ��
)� �	) � = ��
��� � �� = ��. ��
��� � . ����� � 
�) � = �� �� = − �. �
�
�� ��) � = 
��� 
 �� = 
��� 
 . ��� 
 ��) � = �� �� = ��. �� 
�) � = �� �� = �. �
� − �. ���� ��) � = ��
��� 
 �� = ��
��� 
. ����� 
 ��) � = �$� �� �� = ��. �. ���� + ��. $� �. �′ 
!) � = �
 �� = �
 ��) � = �. �� �� = �. �. ����. �′ �!) � = $� � �� = �′� 
��) � = $� 
 �� = �
 �") � = 
�� � �� = ��. ��
 � ��) � = %� �� = ��. %�. $� % 
��) � = %
 �� = %
. $� % �	) � = ��
 � �� = −��. 
�� � ��) � = $��% � �� = ��. $� % 
��) � = 
�� 
 �� = ��
 
 ��) � = �� � �� = ��. 
��� � ��) � = %&�
�� � �� = �√� − �� . �′ 
��) � = ��
 
 �� = − 
�� 
 ��) � = ���� � �� = −��. ��
��� � ��) � = %&���
 � �� = −�√� − �� . �′ 
��) � = �� 
 �� = 
��� 
 �!) � = 
�� � �� = ��. 
�� � . �� � ��) � = %&��� � �� = �� + �� . �′ 
�") � = ���� 
 �� = − ��
��� 
 ��) � = ��
�� � �� = −��. ��
�� �. ���� � �") � = %&�
�� � �� = ��. √�� − � . �′ 
 
Fórmulas de Trigonometria 
 
��
�� 
 = �
�� 
 
�� 
 = ���
 
 
���� 
 = ��� 
 
���� 
 = ��
 
�� 
 
��� 
 + ��
� 
 = � 
��� 
 = � + ��� 
 
��
���
 = � + �����
 
���
 − ��� 
 = � 
�� 
 = 
�� 
��
 
 
�� �−
) = −
�� 
 
��
 �−
) = ()* 
 
 �� �−
) = −�� 
 
��
���
 − �����
 = � 
�� �� + �) = 
�� � . ��
 � + ��
 � . 
�� � 
��
 �� + �) = ��
 � . ��
 � − 
�� � . 
�� � 
�� �� + �) = �� � + �� �� − �� � . �� � 
���� − �) = 
�� � . ��
 � − ��
 � . 
�� � 
��
 �� − �) = ��
 � . ��
 � + 
�� � . 
�� � 
�� �� − �) = �� � − �� �� + �� � . �� � 
�� � . ��
 � = �� +
�� �� + �) + 
�� �� − �), 
()* � . 
�� � = �� +
�� �� + �) − 
�� �� − �), 
��
 � . ��
 � = �� +��
 �� + �) + ��
 �� − �), 
�� � . 
�� � = �� +()* �� − �) − ()* �� + �), 
�� �� = � 
�� � . ��
 � 
��
 �� = ��
� � − 
��� � 
��
 �� = � − � 
��� � 
��
 �� = � ��
� � − � 
�� �� = � �� �� − ��� � 
��� � = � − ��
 ��� 
��
� � = � + ��
 ��� 
�� �� = � − ��
 �
�� � ∴ 
�� �� + ��
 � 
.
�� ��. = /� − ��
 �� 
.��
 ��. = /� + ��
 �� 
�� 01� − 
2 = ()* 
 
�� 01� + 
2 = ()* 
 
�� 3�1� − 
4 = −()* 
 
�� 3�1� + 
4 = −()* 
 
��
 3�1� − 
4 = −
�� 
 
��
 3�1� + 
4 = 
�� 
 
�� ��1 − 
) = −
�� 
 
 
��
 ��1 − 
) = ��
 
 
 
$� � = � $� 
� = $� 
 + $� � $� 
� = $� 
 − $� � 
$� 
� = �. $� 
 $� � = � $� � = $��� � 
$��% 5 = $� 5$� % $��% � = � $�� �� = � $��% 
� = $��% 
 + $��% � $��% % = � � = $��% 
 significa %� = 
 
$��% 
� = $��% 
 − $��% � $�� ��� = � $�� 
 = $���� 
 
$��% 
& = &. $��% 
 
 
 
DIEGO 
 
Fórmulas de Integrais 
 
�) 6 7
 = 
 + � ��) 6 ��
�� 
. ���� 
 7
 = −��
�� 
 + � ��) 6 ��
��� � 7� = −���� � + � ��) 6 
�� � 7� = 89|
�� � + �� �| + � 
�) 6 % 7
 = %
 + � ��) 6 �
 7
 = �
 + � �!) 6 
�� � . �� � 7� = 
�� � + � ��) 6 ��
�� � 7� = 89|��
�� � − ���� �| + � 
�) 6 %
� 7
 = % 
�;�� + � + � ��) 6 7

 = 89|
| + � ��) 6 ��
�� �. ���� � 7� = −��
�� � + � �!) 6 7�%� + �� = �% <=(>? �% + � 
�) 6 
�� 
 7
 = −��
 
 + � ��) 6 % @�
) 7
 = % 6 @�
) 7
 ��) 6 �� 7� = �� + � ��) 6 7�%� − �� = ��% 89 A� + %� − %A + � 
") 6 ��
 
 7
 = 
�� 
 + � ��) 6 �� 7� = ��;�� + � + � ��) 6 7�� = 89|�| + � ��) 6 7��√�� − %� = �% *B(�� �% + � 
	) 6 
��� 
 7
 = �� 
 + � �") 6 
�� � 7� = −��
 � + � ��) 6 � 7� = �� − 6 � 7� ��) 6 7�√%� − �� = *B9�� �% + � 
�) 6 ��
��� 
 7
 = −���� 
 + � �	) 6 ��
 � 7� = 
�� � + � ��) 6 %� 7� = %�89 % + � ��) 6 7�√�� − %� = 89 .� + C�� − %�. + � 
�) 6 
�� 
 . �� 
 7
 = 
�� 
 + � ��) 6 
��� � 7� = �� � + � �") 6 �� � 7� = − 89|��
 �| + � ��) 6 $� � 7� = � $� � − � + � 
!) 6+@��
) + @��
) + ⋯ + @��
), 7
 = 6 @��
) 7
 + 6 @��
) 7
 + ⋯ + @��
) 7
 �	) 6 ���� � 7� = 89|
�� �| + � 8EF∆
 →� @�
 + ∆
) − @�
)∆
 
6 @�
)7
5% = I�5) − I�%) J = 6 C� + @��
)� 7
5
% KJ = �1 6 @�
)C� + @��
)� 7
5
% C%� − 
� → 
 = % 
�� L C%� + 
� → 
 = % �� L 
C
� − %� → 
 = % 
�� L K = 6 @�
) 7
5% M = 1 6 @�
)� 7
5
% M = �1 6 
 @�
) 7
5
% ����) 
�) 6 ���� 
���� 7� �� 6 ������ ��
���� 7� → � = 
� → 6 �� 7� �) 6 ���� 
���� 7� → � � � = 
� → 6 �� 7� 
�) 6 
���� 7� �� 6 ��
���� 7� → � = 
� → 6 � 7� �) N�
)O�
) ��7� N�
) ≤ O�
) → ÷ 
�. �) N�
)O�
) ��7� O�
) > S�
) � O�
�) ≠ O�
�) → 6 N�
)O�
) = 6 K%�
 + 5� + U%�
 + 5� + ⋯ + V%�
 + 5� 7
 
�. �) N�
)O�
) ��7� O�
) > S�
) � O�
) ^ �
 → 6 N�
)�
 − �)�
 + �)���) = 6 K�
 − �) + U�
 + �)� + X�
 + �)� 7
 
�. �) N�
)O�
) ��7� O�
) > S�
) � O�
) = 
� + Y
 + Z → 6 N�
)O�
) = 6 K
 + U�
) + X
� + Y
 + Z 7
 
�. �) N�
)O�
) ��7� O�
) > S�
) � O�
) ^ �
 � O�
) = 
� + Y
 + Z → 6 N�
)O�
) = 6 K
 + U�
) + X
� + Y
 + Z + [�
) + \
� + Y
 + Z 7
 
 
6 
���� 7� = − �� �� + 
����)��
 � + � 6 ��
�� 7� = �� �� + ��
��)
�� � + � 6 ���� 7� = �� ���� + $�|��
 �| + � 
6 ����� 7� = − �� ����� − $�|
�� �| + � 6 
���� 7� = �� 
�� � �� � + �� $�|
�� � + �� �| + � 6 ��
���� 7� = − �� �
� � ��� � + �� $�|�
� � − ��� �| + � 
6 
���� 7� = − �� 
������ ��
 � + � − �� 6 
������ 7� 6 ��
�� 7� = �� ��
���� 
�� � + � − �� 6 ��
���� 7� 6 ���� 7� = �� − � ������ − 6 ������ 7� 
6 ����� 7� = −�� − � ������� − 6 ������� 7� 6 
���� 7� = �� − � �� � 
������ + � − �� − � 6 
������ 7� 6 �
��� 7� = −�� − � ��� � �
����� + � − �� − � 6 �
����� 7� 
6 
���� ��
�� 7� = − 
������ ��
�;��� + � + � − �� + � 6 
������ ��
�� 7� 6 ��%� 7� = �%� �%� − �)�%� + � 
6 �� $� � 7� = $� |$� �| + � 6 7�√�%� − �� = %&���
 0% − �% 2 + � 6 �� �%� 7� = �% �� �%� − �% 6 ���� �%� 7� 
6 7��√%� − �� = − �% $� ]% + √%
� − ��� ] + � 6 7���√%� − �� = − �%�� C%� − �� + � 
 
Dist. P1 P2 7�N�, N�) = C�
� − 
�)� + ��� − ��)� 
P. médio 
_ 3
� + 
�� , �� + ��� 4 
Coeficiente angular m 
� = � − ��
 − 
� 
$`�@�
)→� 
�� @�
)@�
) = � $`�@�
)→� � − ��
 @�
)@�
) = � $`�
→� �� + 
)� 
a = � 
$`�
→b 3� + �
4

 = � $`�@�
)→� %
@�
) − �@�
) = $� % � = @��
). �
 − 
�) + @�
�) 
M = c� K = M� 
 
 
DIEGO

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