Differential Calculus - Comprehensive Study
Notes
Lecture- I
Introduction
Welcome to our Differential Calculus notes. In this comprehensive guide, we will
delve into the essential formulas and concepts of differential calculus. This unit is
vital for mastering advanced topics in mathematics and is tailored to help you grasp
the fundamentals with ease.These notes are lectures wise ,So you can take it from
me anytime through website.
Topics Covered
The Differential Calculus unit comprises four key topics:
1. Differentiation with basic rules
2. Indeterminate forms
3. Series expansion using Taylor and Maclaurin series
4. Radius of curvature
Basic Rules of Differentiation
I. Fundamental Formulas
● Constant Rule: The differentiation of a constant is always zero.
𝑑
○ 𝑑𝑥
(𝑐) = 0
● Identity Rule: The differentiation of x with respect to x is one.
𝑑
○ 𝑑𝑥
(1) = 1
𝑛 𝑛−1
● Power Rule: The differentiation of 𝑥 with respect to x is 𝑛𝑥
𝑑 2
○ 𝑑𝑥
(𝑥 ) = 2𝑥
○
II. Sample Formules
𝑑
● 𝑑𝑥
(1 + 𝑥) = 0 + 1 = 1
Notes
Lecture- I
Introduction
Welcome to our Differential Calculus notes. In this comprehensive guide, we will
delve into the essential formulas and concepts of differential calculus. This unit is
vital for mastering advanced topics in mathematics and is tailored to help you grasp
the fundamentals with ease.These notes are lectures wise ,So you can take it from
me anytime through website.
Topics Covered
The Differential Calculus unit comprises four key topics:
1. Differentiation with basic rules
2. Indeterminate forms
3. Series expansion using Taylor and Maclaurin series
4. Radius of curvature
Basic Rules of Differentiation
I. Fundamental Formulas
● Constant Rule: The differentiation of a constant is always zero.
𝑑
○ 𝑑𝑥
(𝑐) = 0
● Identity Rule: The differentiation of x with respect to x is one.
𝑑
○ 𝑑𝑥
(1) = 1
𝑛 𝑛−1
● Power Rule: The differentiation of 𝑥 with respect to x is 𝑛𝑥
𝑑 2
○ 𝑑𝑥
(𝑥 ) = 2𝑥
○
II. Sample Formules
𝑑
● 𝑑𝑥
(1 + 𝑥) = 0 + 1 = 1
