Скачать или смотреть Successive Differentiation Part 9 | nth Derivative of Rational Functions | B.Sc Maths Sem I | MWSB

🎓 B.Sc. Mathematics (Honours) – Semester I
📘 Chapter 1: Successive Differentiation – Part 9 (nth Derivative of Algebraic Rational Functions)
🏫 University: Ranchi University, Ranchi
📚 Curriculum: As per NEP–FYUGP (Implemented from Session 2025–26 & onwards)
👨‍🏫 Prepared & Explained by: Sandeep Bhatt Sir
(Mathematics Educator | Founder – Om Science Classes, Ranchi)
📺 Channel: Maths With Sandeep Bhatt (MWSB)
📞 Contact: +91-7903262149
📍 Ranchi, Jharkhand
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🧠 Lecture Overview
This lecture covers Part 9 of the chapter Successive Differentiation, focusing on the nth derivative of algebraic rational functions.
You will learn the systematic method for differentiating rational functions by:

Resolving functions into partial fractions
Handling denominators with only linear factors
Applying the standard formula for (x+a)−1(x+a)^{-1}
Deriving results efficiently using the general nth derivative identity

All procedures are explained clearly with step-by-step solved examples.
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📚 Topics Covered in Part 9
1️⃣ Resolving rational functions into partial fractions
2️⃣ nth derivative formula for linear-factor denominators
3️⃣ Application of the standard result:
dndxn(x+a)−1=(−1)nn!(x+a)−(n+1)\frac{d^n}{dx^n}(x+a)^{-1} = (-1)^n n!(x+a)^{-(n+1)}
4️⃣ nth derivative of functions of the form
P(x)(x+a)(x+b),P(x)(ax+b)(cx+d)\frac{P(x)}{(x+a)(x+b)},\quad
\frac{P(x)}{(ax+b)(cx+d)}
5️⃣ Handling rational functions step-by-step through examples
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🧩 Solved Examples in This Lecture
Example 1
y=x+3(x+1)(x+2),find yny = \frac{x+3}{(x+1)(x+2)},\quad \text{find } y_n
Example 2
y=1(x+1)(x+2),find yny = \frac{1}{(x+1)(x+2)},\quad \text{find } y_n
Example 3
y=5(x+2)(x+3),find yny = \frac{5}{(x+2)(x+3)},\quad \text{find } y_n
Example 4
y=x+1(x+2)(x+3),find yny = \frac{x+1}{(x+2)(x+3)},\quad \text{find } y_n
Example 5
y=4x+5(x+2)(2x+1),find yny = \frac{4x+5}{(x+2)(2x+1)},\quad \text{find } y_n
Example 6
y=16x2+11x+3,find yny = \frac{1}{6x^2 + 11x + 3},\quad \text{find } y_n
All examples are solved using the standard nth derivative formula and clean partial fraction decomposition.
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Key Concepts

Partial fraction decomposition
nth derivative of rational functions
Standard nth derivative formula
Successive differentiation of (ax+b)−1(ax+b)^{-1}
Handling linear-factor denominators

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Learning Outcomes
✔ Understand how to resolve rational functions into partial fractions
✔ Apply nth derivative formulas to linear-factor denominators
✔ Derive results quickly using the standard identity
✔ Strengthen concepts of algebraic rational differentiation
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📗 Course Details
Course: B.Sc Mathematics – Semester I
Mode: Online + Offline (Hybrid Learning)
Platform: Maths With Sandeep Bhatt (MWSB)
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👨‍🏫 About the Instructor
Sandeep Bhatt Sir
(Mathematics Educator | Founder – Om Science Classes, Ranchi)
Expertise: Calculus, Differential Equations, Real Analysis
📧 Email: [email protected]
📞 Contact: +91-7903262149
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