Symbolab Derivatives Cheat Sheet
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1
2Symbolab Derivatives Cheat Sheet
Derivative Rules:
Product Rule:
��
Power Rule:
��
��−1
( ��
) = �� ⋅ ��
����
′
′
( �� ⋅ �� )
= ��
⋅ �� + �� ⋅ ��′
��
Derivative of a Constant:
( �� ) = 0
′
′
′
��
��
⋅��−��
⋅��
Quotient Rule: (
����
)
=
Sum/Difference Rule:
2
��
��
���� ( �� )
����
����
′
′
′
Chain Rule:
( �� ± �� )
= ��
± ��
=
⋅
����
����
����
Constant Out: ( �� ⋅ �� )
′
′
= �� ⋅ ��
Common Derivatives:
��
1
��
1
( ln ( �� )) =
( log ( �� )) =
��⋅ln ( 10 )
����
��
����
��
1
��
1
( ln (| �� |)) =
( log
( �� )) =
��
����
��
��⋅ln ( �� )
����
��
��
��
( ��
) = ��
����
Trigonometric Derivatives:
��
��
tan ( �� )
( sin ( �� )) = cos ( �� )
( sec ( �� )) =
����
cos ( �� )
����
��
− cot ( �� )
��
( cos ( �� )) = − sin ( �� )
( csc ( �� )) =
����
sin ( �� )
����
��
2
( tan ( �� )) = sec
( �� )
��
1
( cot ( �� )) = −
����
2
( �� )
����
sin
Arc Trigonometric Derivatives:
��
1
��
1
( arcsin ( �� )) =
( arcsec ( �� )) =
2
2
2
����
√ 1−��
����
√ ��
( ��
−1 )
��
1
��
1
( arccos ( �� )) = −
( arccsc ( �� )) = −
2
����
√ 1−��
2
| �� |√ ��
����
−1
��
1
��
1
( arctan ( �� )) =
( arccot ( �� )) = −
2
����
��
+1
2
����
��
+1
Hyperbolic Derivatives:
��
��
2
( sinh ( �� )) = cosh ( �� )
( tanh ( �� )) = sech
( �� )
����
����
��
��
( cosh ( �� )) = sinh ( �� )
( sech ( �� )) = − sech ( �� ) ⋅ tanh ( �� )
����
����
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