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BASIC DIFFERENTIATION RULES - REVIEWER FOR BOARDS

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๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
[๐‘๐‘ข] = ๐‘๐‘ข′
20)
[๐‘ข ± ๐‘ฃ] = ๐‘ข′ + ๐‘ฃ′
21)
[๐‘ข๐‘ฃ ] = ๐‘ข๐‘ฃ′ + ๐‘ฃ๐‘ข′
22)
๐‘ข
[ ]=
๐‘ฃ๐‘ข′ −๐‘ข๐‘ฃ′
๐‘‘๐‘ฅ ๐‘ฃ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
23)
๐‘ฃ2
[๐‘ ] = 0
24)
[๐‘ข๐‘› ] = ๐‘›๐‘ข๐‘›−1 ๐‘ข′
25)
[๐‘ฅ ] = 1
26)
[|๐‘ข|] =
[๐‘™๐‘›๐‘ข] =
๐‘ข
|๐‘ข|
(๐‘ข ′ ), ๐‘ข ≠ 0
27)
๐‘ข′
28)
๐‘ข
[๐‘’ ๐‘ข ] = ๐‘’ ๐‘ข ๐‘ข′
[๐‘™๐‘œ๐‘”๐‘Ž ๐‘ข] =
29)
๐‘ข′
30)
(๐‘™๐‘›๐‘Ž)๐‘ข
[๐‘Ž๐‘ข ] = (๐‘™๐‘›๐‘Ž)๐‘Ž๐‘ข ๐‘ข′
31)
[sin ๐‘ข] = (cos ๐‘ข)๐‘ข′
32)
[cos ๐‘ข] = −(sin ๐‘ข)๐‘ข′
33)
[tan ๐‘ข] = (๐‘ ๐‘’๐‘ 2 ๐‘ข)๐‘ข′
34)
[cot ๐‘ข] = −(๐‘๐‘ ๐‘ 2 ๐‘ข)๐‘ข′
35)
[sec ๐‘ข ] = (sec ๐‘ข tan ๐‘ข)๐‘ข′
36)
[csc ๐‘ข ] = −(csc ๐‘ข cot ๐‘ข)๐‘ข′
37)
[arcsin ๐‘ข] =
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
๐‘‘
๐‘‘๐‘ฅ
−๐‘ข′
[arccos ๐‘ข] =
√1−๐‘ข2
๐‘ข′
[arctan ๐‘ข] =
[arccot ๐‘ข] =
1+๐‘ข2
−๐‘ข′
1+๐‘ข2
๐‘ข′
[arcsec ๐‘ข] =
[arccsc ๐‘ข] =
|๐‘ข|√๐‘ข2 −1
−๐‘ข′
|๐‘ข|√๐‘ข2 −1
[sinh ๐‘ข] = (cosh ๐‘ข)๐‘ข′
[cosh ๐‘ข] = (sinh ๐‘ข)๐‘ข′
[tanh ๐‘ข] = (๐‘ ๐‘’๐‘โ„Ž2 ๐‘ข)๐‘ข′
[coth ๐‘ข] = −( ๐‘๐‘ ๐‘โ„Ž2 ๐‘ข)๐‘ข′
[sech ๐‘ข] = −(sech ๐‘ข tanh ๐‘ข)๐‘ข′
[csch ๐‘ข] = −(csch ๐‘ข coth ๐‘ข)๐‘ข′
[๐‘ ๐‘–๐‘›โ„Ž−1 ๐‘ข] =
[๐‘๐‘œ๐‘ โ„Ž−1 ๐‘ข] =
[๐‘ก๐‘Ž๐‘›โ„Ž−1 ๐‘ข] =
[๐‘๐‘œ๐‘กโ„Ž−1 ๐‘ข] =
[๐‘๐‘œ๐‘ โ„Ž−1 ๐‘ข] =
[๐‘ ๐‘’๐‘โ„Ž−1 ๐‘ข] =
[๐‘๐‘ ๐‘โ„Ž−1 ๐‘ข] =
๐‘ข′
√๐‘ข2 +1
๐‘ข′
√๐‘ข2 −1
๐‘ข′
1−๐‘ข2
๐‘ข′
1−๐‘ข2
๐‘ข′
√๐‘ข2 −1
−๐‘ข′
๐‘ข√1−๐‘ข2
๐‘ข′
|๐‘ข|√1+๐‘ข2
๐‘ข′
√1−๐‘ข2
Source: Calculus 10th Edition (Ron Larson and Bruce Edwards)
Tecson, Ameg G. - Reviewer
Tecson, Ameg G. - Reviewer
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