Unlock the Power
𝑑𝑦 of Derivatives
Dive into the world of calculus with this
complete, visually engaging guide to
derivative rules. Packed with step-by-
step proofs, colourful graphs, solved
𝑑𝑥 examples, and plenty of practice
questions, these notes make learning
derivatives easy, intuitive, and fun.
Whether you're a student aiming for top
• Constant Rule
grades or a teacher seeking a clear
• Power Rule
reference, this guide will turn complex
• Constant Multiple Rule concepts into simple, memorable ideas.
• Sum and Difference Rule Master the rules, see the patterns, and
• Product Rule boost your problem-solving skills all in
• Quotient Rule one beautifully crafted notebook.
• Chain Rule
The Formulae
of
Derivatives
Written by SHAH DOST
, THE FORMULAE OF DERIVATIVES
Contents
Constant Rule ............................................................... 3
Power Rule ................................................................... 6
Constant Multiplication Rule ...................................... 9
Sum and Difference Rule........................................... 12
Product Rule............................................................... 15
Chain Rule ................................................................. 24
ENDING NOTE ......................................................... 28
1
, THE FORMULAE OF DERIVATIVES
The most important rules of derivatives
• Constant Rule
𝑑
ሺ𝑐ሻ = 0
𝑑𝑥
• Power Rule
𝑑 𝑛
ሺ𝑥 ሻ = 𝑛𝑥 𝑛−1
𝑑𝑥
• Constant Multiplication Rule
𝒅 𝑑
ൣ𝒄. 𝒇ሺ𝒙ሻ൧ = 𝑐. 𝑓ሺ𝑥ሻ
𝒅𝒙 𝑑𝑥
• Sum and Difference Rule
𝑑 𝑑 𝑑
ൣ𝑓ሺ𝑥ሻ ± 𝑔ሺ𝑥ሻ൧ = 𝑓ሺ𝑥ሻ ± 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥 𝑑𝑥
• Product Rule
𝑑 𝑑 𝑑
ൣ𝑓ሺ𝑥ሻ𝑔ሺ𝑥ሻ൧ = 𝑔ሺ𝑥ሻ 𝑓ሺ𝑥ሻ + 𝑓ሺ𝑥ሻ 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥 𝑑𝑥
• Quotient Rule
𝑑 𝑑
𝑑 𝑓ሺ𝑥ሻ 𝑔ሺ𝑥ሻ 𝑓ሺ𝑥ሻ − 𝑓ሺ𝑥ሻ 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥
ቈ = 2
𝑑𝑥 𝑔ሺ𝑥ሻ ൣ𝑔ሺ𝑥ሻ൧
• Chain Rule
𝑑 𝑑 𝑑
ൣ𝑓ሺ𝑔ሺ𝑥ሻሻ൧ = 𝑓 ቀ𝑔ሺ𝑥ሻቁ . 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥 𝑑𝑥
2
𝑑𝑦 of Derivatives
Dive into the world of calculus with this
complete, visually engaging guide to
derivative rules. Packed with step-by-
step proofs, colourful graphs, solved
𝑑𝑥 examples, and plenty of practice
questions, these notes make learning
derivatives easy, intuitive, and fun.
Whether you're a student aiming for top
• Constant Rule
grades or a teacher seeking a clear
• Power Rule
reference, this guide will turn complex
• Constant Multiple Rule concepts into simple, memorable ideas.
• Sum and Difference Rule Master the rules, see the patterns, and
• Product Rule boost your problem-solving skills all in
• Quotient Rule one beautifully crafted notebook.
• Chain Rule
The Formulae
of
Derivatives
Written by SHAH DOST
, THE FORMULAE OF DERIVATIVES
Contents
Constant Rule ............................................................... 3
Power Rule ................................................................... 6
Constant Multiplication Rule ...................................... 9
Sum and Difference Rule........................................... 12
Product Rule............................................................... 15
Chain Rule ................................................................. 24
ENDING NOTE ......................................................... 28
1
, THE FORMULAE OF DERIVATIVES
The most important rules of derivatives
• Constant Rule
𝑑
ሺ𝑐ሻ = 0
𝑑𝑥
• Power Rule
𝑑 𝑛
ሺ𝑥 ሻ = 𝑛𝑥 𝑛−1
𝑑𝑥
• Constant Multiplication Rule
𝒅 𝑑
ൣ𝒄. 𝒇ሺ𝒙ሻ൧ = 𝑐. 𝑓ሺ𝑥ሻ
𝒅𝒙 𝑑𝑥
• Sum and Difference Rule
𝑑 𝑑 𝑑
ൣ𝑓ሺ𝑥ሻ ± 𝑔ሺ𝑥ሻ൧ = 𝑓ሺ𝑥ሻ ± 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥 𝑑𝑥
• Product Rule
𝑑 𝑑 𝑑
ൣ𝑓ሺ𝑥ሻ𝑔ሺ𝑥ሻ൧ = 𝑔ሺ𝑥ሻ 𝑓ሺ𝑥ሻ + 𝑓ሺ𝑥ሻ 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥 𝑑𝑥
• Quotient Rule
𝑑 𝑑
𝑑 𝑓ሺ𝑥ሻ 𝑔ሺ𝑥ሻ 𝑓ሺ𝑥ሻ − 𝑓ሺ𝑥ሻ 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥
ቈ = 2
𝑑𝑥 𝑔ሺ𝑥ሻ ൣ𝑔ሺ𝑥ሻ൧
• Chain Rule
𝑑 𝑑 𝑑
ൣ𝑓ሺ𝑔ሺ𝑥ሻሻ൧ = 𝑓 ቀ𝑔ሺ𝑥ሻቁ . 𝑔ሺ𝑥ሻ
𝑑𝑥 𝑑𝑥 𝑑𝑥
2
