Скачать или смотреть 12th Maths - Differentiation - Day 01 | CA KARAN KABRA

CA Karan Kabra
(CA, DISA, PGDIFM, CAIIB, M. Com, B. Com, DB&F, NET, SET)

All India Topper in Mathematics in CA (Scored 100%)
All India Topper in Statistics in CA (Scored 100%)
Winner of K.V. Chandramouli Memorial Prize “Best Paper Award” in Mathematics in CA
Winner of Ganeshmal Patni Memorial Prize “Best Paper Award” in Statistics in CA
All India Rank (AIR) 24th in CS Executive
1st in Maths in 12th Board (Scored 100%)

CA Karan Kabra has been in teaching field since 2013. In this span, he has taught over 8000 students the subject of Cost Accounting and Mathematics from 11th Std up to Chartered Accountancy Course.

The video "12th Maths - Differentiation - Day 01" primarily covers the revision of 11th-grade differentiation basics. The speaker confirms that the 12th-grade material has not yet begun within this specific session.
The main topics covered include:
I. Introduction to Differentiation
• Definition of Differentiation: Differentiation is the process of finding the derivative.
• Meaning of Derivative: A derivative represents the rate of change—how one quantity changes in response to another.
• Context: The material is a continuation of the last chapter of Part One from the 11th standard.
• Future Application: The utility of derivatives will be discussed in the subsequent chapter, Application of Derivatives.
II. Notation The video discusses different ways to denote the derivative:
• dy/dx: Denotes the derivative of y with respect to x (Derivative of y with respect to x).
• f′(x): Used when the function is denoted as f(x).
• y′.
• y1.
III. Basic Formulae of Derivatives Memorization of these formulae is mandatory. The specific formulae covered include:
• Derivative of any constant (k) is zero.
• Derivative of x is 1.
• Derivative of kx is k.
• Derivative of xn is n⋅x^(n−1).
• Derivative of logx is 1/x.
• Derivative of 1/x is −1/x^2.
• Derivative of x is 1/(2x).
• Derivative of ax is ax⋅loga.
• Derivative of e^x is e^x.
IV. Rules of Differentiation The rules governing how derivatives are calculated for combined functions are introduced:
• Addition and Subtraction Rule (y=u±v): The derivative is the sum or difference of the individual derivatives (dy/dx=du/dx±dv/dx).
• Multiplication Rule (Product Rule) (y=u⋅v): The formula is u⋅(Derivative of v)+v⋅(Derivative of u).
• Constant Multiple Rule (y=k⋅u): If a constant (k) is in multiplication with a function (u), the constant remains as it is, and the derivative is taken only of the function (k⋅du/dx).
◦ Contrast: If a constant is alone (e.g., y=k), its derivative is zero.
• Triple Product Rule (y=u⋅v⋅w): The derivative is calculated by taking the derivative of one function at a time while keeping the other two constant, and summing the results.
• Division Rule (Quotient Rule) (y=u/v): The formula is (v⋅(Derivative of u)−u⋅(Derivative of v))/v2 (starting with the denominator).
V. Practice Examples (Revision) The video provides several examples applying the basic formulae and rules, covering scenarios such as:
• Finding the derivative of xn.
• Finding the derivative when a constant is multiplying a function (k⋅u).
• Finding the derivative of sums and differences of terms.
• Rewriting expressions (e.g., 1/x4 as x−4) to use the xn formula.
• Applying the Product Rule (u⋅v).
• Applying the Triple Product Rule (u⋅v⋅w).
• Applying the Quotient Rule (u/v).