Class 12 Chapter 5 Derivatives Continuity and Differentiability in One Shot 🔥

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  • Опубліковано 4 лют 2025

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  • @apexlegends4656
    @apexlegends4656 10 днів тому +3

    00:37 Introduction and class overview on derivatives and continuity.
    01:30 Derivatives understanding boosts performance in advanced calculus topics.
    03:20 Understanding differentiability through LH and RH limits.
    04:14 Understanding differentiation limits and correcting formulas in derivatives.
    05:56 Understanding the properties of the greatest integer function.
    06:46 Understanding the greatest integer function and its properties.
    08:42 Understanding the Greatest Integer Function and its notation.
    09:28 Understanding the Floor Function and its Application in Derivatives.
    11:30 Understanding function values with substitution method.
    12:24 Understanding limits and properties of greatest integer function.
    14:18 Evaluating limits using substitution in derivatives.
    15:09 Understanding limits approaching zero in derivatives.
    16:55 Live interaction enhances learning in calculus derivatives and continuity.
    17:41 Understand critical points and differentiability of the modulus function.
    19:21 Deriving values of x using limits and handling absolute functions.
    20:09 Understanding differentiability through right-hand derivatives (RHD) using specific formulas.
    21:50 Understanding the limit of a function as h approaches zero.
    22:38 Understanding the formula for Left-Hand Derivative (LHD).
    24:31 Understanding limits and continuity in derivatives.
    25:27 Understanding continuity and differentiability of specific functions.
    27:17 Understanding the continuity of functions with decimal inputs.
    28:07 Understanding the continuity of greatest integer functions.
    29:40 Left-hand limit is essential for continuous functions.
    30:30 Understanding left-hand and right-hand limits in calculus.
    32:19 Understanding the application of limits in calculus problems.
    33:06 Key limit formulas essential for continuity and differentiability.
    34:56 Numerical problems require shortcuts for efficiency in exams.
    35:44 Key techniques for substituting values in derivative problems.
    37:25 Discussion on answering a specific continuity question.
    38:10 Understanding continuity through limits in functions.
    39:53 Understanding continuity through limits and decision-making criteria.
    40:46 Understanding limits: Left-hand limit (LHL) and right-hand limit (RHL) equality.
    42:18 Understanding limits and continuity in derivatives at x = 0.
    43:12 Understand the importance of proper notation in derivatives and limits.
    44:59 Exploring continuity and limits in functions.
    45:42 Understanding limits involving exponential functions and their indeterminate forms.
    47:23 Explaining limits and derivatives using the exponential function.
    48:19 Exploring limits as x approaches infinity using exponential functions.
    49:58 Understanding discontinuity of a function at x = 0.
    50:50 Understanding derivatives through limits using specific examples.
    52:22 Understanding continuity in functions and the role of limit values.
    53:11 Understanding the application of limits in calculating derivatives.
    54:45 Understanding limits using LHL and rationalization techniques.
    55:27 Understanding sign changes in rational equations for derivatives.
    57:22 Finding limits using right-hand limit and function value.
    58:09 Understanding continuity through limits in functions.
    59:46 Limit and power simplification in calculus.
    1:00:32 Simplifying expressions using identities and powers of 2.
    1:02:15 Understanding the concept of limits and identities in derivatives.
    1:03:02 Limits lead to the determination of k value in derivatives.
    1:04:35 Understanding continuity and the role of k in function values.
    1:05:18 Understanding limits in trigonometric derivatives as x approaches 0.
    1:07:56 Understanding the formula for limits involving kx².
    1:08:50 Deriving limits using formulas and evaluating expressions.
    1:10:37 Understanding continuity and differentiability using three key blocks.
    1:11:26 Understand limits as h approaches 0 in derivatives.
    1:13:35 Understanding limits as h approaches 0 in derivatives.
    1:14:28 Understanding the continuity and differentiability concept in derivatives.
    1:16:02 Explains the process of evaluating limits with substitutions.
    1:17:02 Deriving limits for continuity using right-hand limits.
    1:18:50 Discussion on continuity problems and finding function values.
    1:19:34 Understanding right-hand limits and calculations in derivatives.
    1:21:11 Understanding limits and derivatives in the context of continuity.
    1:21:57 Understanding derivatives through algebraic manipulation.
    1:23:51 Understanding continuity through left-hand and right-hand limits.
    1:24:33 Exploring limits and solving the 0/0 indeterminate form using long division.
    1:26:19 Understanding limits and transformations in derivatives.
    1:27:14 Simplifying derivatives using limits and identifying equations.
    1:28:45 Discussing left-hand limits in derivative calculations.
    1:29:48 Understanding derivatives with limits as h approaches zero.
    1:31:35 Understanding the differentiation formulas for cubic expressions.
    1:32:38 Understanding limits is crucial for solving derivative problems.
    1:34:32 Understanding limits and derivatives through bracket manipulation.
    1:35:17 Understanding the application of squares in derivatives.
    1:36:49 Understanding the values of A and B in derivatives.
    1:37:47 Correction of errors in derivative calculations explained step-by-step.
    1:39:25 Understanding limits for continuity and differentiability in derivatives.
    1:40:12 Understanding limits and continuity in derivatives with examples.
    1:42:56 Simplifying square roots and using limits in derivatives.
    1:44:18 Solving equations with variable substitutions.
    1:45:59 Understanding continuity in functions and its implications.
    1:46:44 The function is continuous between 0 and 1.
    1:48:48 Discussion on continuity and derivatives in the class.
    1:49:33 Understanding redefinition of functions in continuity, specifically the modulus function.
    1:51:09 Understanding modular functions and their continuity across different cases.
    1:51:50 Understanding Modulus and Its Impact on Negative Values
    1:53:38 Understanding continuity of functions and solving modulus problems.
    1:54:37 Understanding limits with repeated values at specific points.
    1:56:11 Understanding continuity and its relation to derivatives.
    1:57:12 Break announced before continuing derivatives discussion.
    2:08:52 Introduction to the derivatives session with essential formulas.
    2:10:04 Introduction to derivatives with a focus on foundational concepts.
    2:11:53 Understanding derivatives and constants in logarithmic functions.
    2:13:28 Understanding logarithmic functions and their derivatives is crucial.
    2:15:13 Understanding the rules for logarithmic differentiation in derivatives.
    2:16:08 Understanding derivatives using logarithmic and normal functions.
    2:18:15 Understanding logarithmic differentiation for derivatives.
    2:19:02 Understanding derivatives and their basic rules of differentiation.
    2:21:01 Understanding derivatives without using logarithms.
    2:21:57 Key techniques for solving derivatives and their applications.
    2:24:22 Understanding the importance of brackets in derivatives.
    2:25:13 Understanding derivatives and their application in differentiability.
    2:27:36 Understanding logarithmic differentiation using product rule.
    2:28:44 Integration of derivatives and key concepts explained.
    2:30:33 Explores the importance of detailed question-solving in derivatives.
    2:31:19 Understanding derivatives of power functions and logarithmic functions.
    2:33:49 Understanding the function x^x and its derivatives.
    2:35:10 Understanding variable power in functions and domain extraction.
    2:36:59 Understanding the application of the chain rule in derivatives.
    2:37:56 Understanding logarithmic expressions with proper notation.
    2:39:39 Exploring the behavior of exponential functions iteratively.
    2:40:31 Learning to remove infinity in calculus using logarithmic differentiation.
    2:43:49 Discusses important logarithmic problems in derivatives.
    2:44:40 Understanding numerical values in derivatives using variables m, n, p, and q.
    2:46:13 Understanding properties of logarithmic functions during differentiation.
    2:47:34 Understanding the multiplication rules in derivatives.
    2:51:02 Understanding derivatives with emphasis on numerator and denominator differentiation.
    2:52:28 Exploring logarithmic equations in derivatives and their systematic solutions.
    2:53:58 Understanding logarithmic properties in derivatives.
    2:54:53 Understanding derivatives through common factors and logarithmic properties.
    2:57:10 Understanding derivatives using common factors in expressions.
    2:58:29 Simplified method for derivatives using logarithms.
    3:00:33 Learn a new method for solving derivatives effectively.

    • @apexlegends4656
      @apexlegends4656 10 днів тому +1

      3:01:20 Solving logarithmic derivatives using variable powers.
      3:03:18 Concepts of logarithmic derivatives and their calculations.
      3:04:16 Derivatives of logarithmic functions using product rule and simplification.
      3:06:17 Understanding the role of brackets in derivatives and logarithmic functions.
      3:07:21 Understanding the derivative of 1/x using product and quotient rules.
      3:09:37 Understanding derivatives through step-by-step differentiation techniques.
      3:10:37 Understanding derivatives and logarithmic differentiation techniques.
      3:12:21 Understanding derivatives through practical examples.
      3:13:19 Explaining logarithmic functions and variable substitution in derivatives.
      3:15:12 Understanding the product rule for differentiability in three functions.
      3:16:06 Understanding derivatives involving logarithmic functions and brackets.
      3:17:53 Understanding logarithmic differentiation methods for derivative problems.
      3:18:48 Understanding the differentiation of logarithmic functions.
      3:21:34 Understanding when to use logarithms in calculus problems.
      3:22:39 Understanding the use of equality symbols in logarithmic expressions.
      3:24:35 Understanding derivatives involving logarithmic functions.
      3:25:37 Understanding derivatives involving division and applying rules effectively.
      3:28:29 Exploring derivatives through integration and parameterization techniques.
      3:29:17 Understanding derivatives involving logarithmic and power functions.
      3:32:00 Importance of short breaks during long study sessions.
      3:39:50 Introduction to the session with high energy and enthusiasm.
      3:42:47 Understanding derivatives with respect to common variables in parametric form.
      3:43:54 Understanding derivatives and differentiability in parametric forms.
      3:49:18 Understanding power rules for derivatives in calculus.
      3:50:27 Understanding and solving parametric forms in derivatives.
      3:52:36 Understanding derivatives using brackets for safety in calculations.
      3:53:59 Understanding double derivatives through single derivatives.
      3:57:09 Parametric form and double derivative calculations in detail.
      3:59:24 Understanding derivatives through squaring and simplifying expressions.
      4:01:34 Understanding second derivatives and their invariance under transformations.
      4:03:15 Understanding and solving parametric equations in derivatives.
      4:05:32 Understanding derivatives and their application in problems
      4:06:22 Key concepts of derivatives and calculations in continuity and differentiability.
      4:09:06 Understanding the relationship between functions and their derivatives.
      4:09:55 Understanding differentiability through derivative examples.
      4:12:19 Implicit functions mix variables x and y.
      4:13:04 Understanding implicit differentiation in derivatives.
      4:16:17 Simplifying differentiation by manipulating terms for easier calculation.
      4:17:22 Understanding derivatives through practical examples and rules.
      4:19:15 Understanding derivatives and their calculations with brackets.
      4:20:19 Understanding the formula for derivatives and continuity.
      4:22:22 Explains the exclusion of constant 'a' from derivatives to simplify calculations.
      4:23:15 Understanding the differentiation of trigonometric identities.
      4:26:17 Understanding derivatives through proofs and examples.
      4:27:53 Understanding differentiation involving exponential functions and logarithms.
      4:29:58 Understanding the manipulation of exponential functions in derivatives.
      4:31:01 Understanding derivatives of exponential functions.
      4:32:52 Understanding the process of solving derivatives with common approaches.
      4:33:46 Explores common factors and manipulations in exponentials for derivatives.
      4:35:38 Understanding a challenging derivative problem from previous CBSE exams.
      4:36:25 Understanding derivatives, continuity, and differentiability concepts.
      4:38:33 Explaining value substitutions for derivative calculations.
      4:39:58 Exploration of derivatives using a specific mathematical question.
      4:42:20 Understanding derivatives through transformations in roots and powers.
      4:43:14 Understanding the approach for derivatives using powers and substitution.
      4:45:09 Understanding the process of finding derivatives and their relationships.
      4:47:29 Explaining the steps for solving derivative questions.
      4:49:31 Explains product rule for derivatives in depth.
      4:50:22 Understanding multipliers and derivatives in calculus problems.
      4:52:14 Understanding derivatives of composite functions and their simplification.
      4:53:11 Understanding derivatives using the product and quotient rules.
      4:55:23 Understanding derivatives and their properties through complex problems.
      4:56:18 Understanding derivatives and their application in logarithmic functions.
      4:58:09 Calculating derivatives using LCM techniques.
      4:59:02 Explains derivatives with chain rule and product rule application.
      5:01:40 Understanding double derivatives and their implications in continuity.
      5:02:39 Derivatives and simplification in calculus are made easy with step-by-step methods.
      5:04:28 Understanding derivatives using chain rule and properties of exponentials.
      5:05:28 Understanding the application of derivatives through example.
      5:07:26 Understanding derivatives through practical problem-solving techniques.
      5:08:17 Understanding derivatives through repeated differentiation.
      5:10:16 Understanding derivatives using double and single derivative substitutions.
      5:11:21 Understanding exponential forms and simplification in derivatives.
      5:13:28 Understanding derivatives using exponential and polynomial functions.
      5:14:17 Solving a complex derivative problem step-by-step.
      5:16:14 Derivatives and differentiation rules applied to an equation.
      5:17:11 Understanding derivatives and their calculations in a simple manner.
      5:19:11 Understanding derivatives using product rule and standard functions.
      5:20:11 Understanding derivatives by substituting values for simplification.
      5:22:11 Understanding inverse trigonometric functions and their importance across chapters.
      5:22:58 Understanding rules for substitution in inverse function problems.
      5:24:42 Key trigonometric identities are essential for solving derivatives problems.
      5:25:41 Understanding trigonometric identities and transformations in derivatives.
      5:27:46 Understanding derivatives with trigonometric functions and their differentiability.
      5:28:51 Understanding the transformations in derivatives with power functions.
      5:30:52 Understanding domain and range through specific functions.
      5:31:42 Understanding derivatives and inverse functions in calculus.
      5:33:31 Understanding derivatives with trigonometric identities.
      5:34:28 Understanding differentiability and solving related questions.
      5:36:27 Understanding derivatives and continuity through application of formulas.
      5:37:30 Understanding derivatives in differentiability problems.
      5:39:20 Understanding inverse trigonometric functions and their derivatives.
      5:40:28 Derivatives involve trigonometric identities for sine and cosine.
      5:42:42 Understanding derivatives and differentiability concepts with examples.
      5:43:53 Understanding derivatives and inverse trigonometric functions.
      5:46:22 Key strategies for solving limits involving square roots.
      5:47:24 Understanding LCM and trigonometric identities for derivatives.
      5:49:15 Understanding the concept of assigning values in derivatives.
      5:50:14 Understanding the application of formulas in derivatives and trigonometric functions.
      5:52:25 Understanding derivatives and continuity in calculus.
      5:53:14 Differentiability implies continuity in functions.

    • @BKMathurMathsDelhi
      @BKMathurMathsDelhi  10 днів тому +1

      My god...well done bro❤️❤️

    • @AryanThakur_ig
      @AryanThakur_ig 9 днів тому

      Thankyou you bro

  • @abhaytandon6066
    @abhaytandon6066 10 днів тому +7

    Thank you sir for this video all concepts are crystal clear 🙏👌🌞👏🙌 you are the best.

  • @Navyajain-2797
    @Navyajain-2797 10 днів тому +4

    Best for the revision of ch 5 and really helps in brushing up all the concepts ... Thank you so much for this wonderful session and efforts ❤️

  • @tanishasharma011
    @tanishasharma011 10 днів тому +4

    Such a amazing session of derivative, continuity and differentiability sir.... Thank u so much sir 😊.... This chapter is now fixed in my mind sir !!! Bss ab board exam mein rock krna hai maths ka paper.

  • @Versaudey
    @Versaudey 9 днів тому +2

    Sir itni mehnat to shyd hi koi krta hoga jitni aap krte ho apne students ke liye thank you very much sir 🫡🫡 salute

  • @khyatiyadavv
    @khyatiyadavv 10 днів тому +3

    this lecture is sooo good and sir this is a reflection of your hardwork..you invest so much time for us students..literally to grateful to have you as our maths teacher❤💫

  • @Abhipshaaa11
    @Abhipshaaa11 10 днів тому +3

    Best video lecture for ch 5 💯 Thankyou so much sir for investing your time and strength in teaching one of the most important chapters. All the concepts were completely understandable.

  • @tanyasharma9487
    @tanyasharma9487 10 днів тому +2

    Thank you sir for this amazing lecture and Thank you for your efforts 🙏🏻 My concepts are clear NOW 😊

  • @ShaunSteni
    @ShaunSteni 8 днів тому +1

    Sir I'm watching this for the second time to practice the chapter properly. Thank you sir for your efforts

  • @AarushIsdumb
    @AarushIsdumb 10 днів тому +2

    Lecture was worth it! Truly

  • @Varunn-xd
    @Varunn-xd 10 днів тому +2

    Another lit session dedication on peak..🔥🔥

  • @SanskritiPandey-xj1tu
    @SanskritiPandey-xj1tu 10 днів тому +2

    Thankyou so much sir for such a wonderful lecture....😊

  • @LEGENDYTSHORTS
    @LEGENDYTSHORTS 10 днів тому +6

    Sir salute almost 6 hour ki video bnane ke liye

  • @anshroy282
    @anshroy282 10 днів тому +3

    Had a Nice interactive experience 👍

  • @tanishapradeep5300
    @tanishapradeep5300 10 днів тому +2

    Thank you so much sir for your support and guidance 🙏🏻
    Sir all doubts are clear and again thank you sir for the best class 💗🙏🏻

  • @navyajain1772
    @navyajain1772 10 днів тому +2

    Thankyou sir for this video, pura chapter ache se cover hogya😁

  • @VishalParjapati-zp3my
    @VishalParjapati-zp3my День тому +1

    🇮🇳🇮🇳

  • @KhushiGuptah
    @KhushiGuptah 10 днів тому +2

    Thankyou so much for your efforts sir 🙏🏻

  • @Kshagrwl30
    @Kshagrwl30 10 днів тому +3

    Thankyou so much for your efforts sir , it was damm good video❤️🙏

  • @Ranbir-su8bw
    @Ranbir-su8bw 10 днів тому +2

    Thankyou sir , the whole lecture is very helpful and informative!
    Grateful for it .

  • @SoumyaChoudhary-v9v
    @SoumyaChoudhary-v9v 10 днів тому +2

    6 hour ki mehnat humare liye
    Jay bharat
    Jay mathur sir ❤

  • @BrijeshNath-yq7jc
    @BrijeshNath-yq7jc 9 днів тому +1

    Jo video ko like karega Bhagwan Kasam 95+ laaega or jo share karega 98+ lagega $DON'T TAKE RISK$

  • @PiyushGupta-bg2ic
    @PiyushGupta-bg2ic 10 днів тому +2

    Sir superb lecture next konsa ch?

  • @cakkgupta
    @cakkgupta 10 днів тому +2

    sir please integration

  • @LEGENDYTSHORTS
    @LEGENDYTSHORTS 10 днів тому +3

    Sir almost 6 hour ki video dekhne ke baad to me bhi shaheed ho gya
    Me be like :finally one more chapter completed
    Thanks for your hardwork

  • @AryanThakur_ig
    @AryanThakur_ig 9 днів тому

    1:46:17

  • @BrijeshNath-yq7jc
    @BrijeshNath-yq7jc 10 днів тому +3

    Jo video ko like nai karega... bhagwan kasam fail ho jaega

    • @BKMathurMathsDelhi
      @BKMathurMathsDelhi  10 днів тому

      😂😂🙏nai nai aisa mat bol...this is wrong...koi fail nai hoga sab pass honge