GENERAL DERIVATIVE RULES
Constant Rule
Constant Multiple Rule
Sum Rule
Difference Rule
Product Rule
Quotient Rule
Chain Rule
π
[π] = 0
ππ₯
π
[ππ(π₯)] = ππ ′ (π₯)
ππ₯
π
[π(π₯) + π(π₯)] = π ′ (π₯) + π′ (π₯)
ππ₯
π
[π(π₯) − π(π₯)] = π ′ (π₯) − π′ (π₯)
ππ₯
π
[π(π₯) β π(π₯)] = π ′ (π₯)π(π₯) + π(π₯)π′ (π₯)
ππ₯
π π(π₯)
π(π₯)π ′ (π₯) − π(π₯)π′ (π₯)
[
]=
[π(π₯)]2
ππ₯ π(π₯)
π
[π(π(π₯))] = π ′ (π(π₯))π′ (π₯)
ππ₯
DERIVATIVE RULES FOR PARTICULAR FUNCTIONS
FUNCTION
BASIC RULE
Power
Sine
Cosine
Tangent
Cosecant
Secant
Cotangent
Arcsine
Arccosine
Arctangent
Arccosecant
Arcsecant
Arccotangent
Exponential (base e)
Exponential (base a)
Natural Logarithm
Logarithm (base a)
CHAIN RULE
π π
[π₯ ] = ππ₯ π−1
ππ₯
TRIGONOMETRIC FUNCTIONS
π
[sin(π₯)] = cos(π₯)
ππ₯
π
[cos(π₯)] = −sinβ‘(π₯)
ππ₯
π
[tan(π₯)] = sec 2 (π₯)
ππ₯
π
[csc(π₯)] = β‘ − csc(π₯) cotβ‘(π₯)
ππ₯
π
[sec(π₯)] = β‘ sec(π₯) tanβ‘(π₯)
ππ₯
π
[cot(π₯)] = − csc 2 (π₯)
ππ₯
INVERSE TRIGONOMETRIC FUNCTIONS
π
1
sin−1 (π₯) = β‘
ππ₯
√1 − π₯ 2
π
−1
cos −1 (π₯) = β‘
ππ₯
√1 − π₯ 2
π
1
tan−1 (π₯) = β‘
ππ₯
1 + π₯2
π
−1
csc −1 (π₯) = β‘
ππ₯
|π₯|√π₯ 2 − 1
π
[csc(π’)] = β‘ − csc(π’) cotβ‘(π’) β π’′
ππ₯
π
[sec(π’)] = β‘ sec(π’) tanβ‘(π’) β‘ β π’′
ππ₯
π
[cot(π’)] = − csc 2 (π’) β π’′
ππ₯
π
1
sec −1 (π₯) = β‘
ππ₯
|π₯|√π₯ 2 − 1
π
1
sec −1 (π’) = β‘
β π’′
ππ₯
|π’|√π’2 − 1
π
−1
cot −1 (π₯) = β‘
ππ₯
1 + π₯2
EXPONENTIAL FUNCTIONS
π π₯
[π ] = π π₯
ππ₯
π π₯
[π ] = π π₯ ln(π)
ππ₯
LOGARITHMIC FUNCTIONS
π
1
[ln(π₯)] =
ππ₯
π₯
π
1
[log π (π₯)] =
ππ₯
π₯ β ln(π)
π
−1
cot −1 (π’) = β‘
β π’′
ππ₯
1 + π’2
Created by Sarah Carter | @mathequalslove |mathequalslove.net |
π π
[π’ ] = ππ’π−1 β π’′
ππ₯
π
[sin π’] = cos(π’) β π’′
ππ₯
π
[cos π’] = −sin(π’) β π’′
ππ₯
π
[tan(π’)] = sec 2 (π’) β π’′
ππ₯
π
1
sin−1 (π’) = β‘
β π’′
ππ₯
√1 − π’2
π
−1
cos −1 (π’) = β‘
β π’′
ππ₯
√1 − π’2
π
1
tan−1 (π’) = β‘
β π’′
ππ₯
1 + π’2
π
−1
csc −1 (π’) = β‘
β π’′
ππ₯
|π’|√π’2 − 1
π π’
[π ] = π π’ β π’′
ππ₯
π π’
[π ] = ππ’ ln(π) β π’′
ππ₯
π
1
π’′
[ln(π’)] = β π’′ β‘ππβ‘
ππ₯
π’
π’
π
1
[log π (π’)] =
β π’′
ππ₯
π’ β ln(π)
