Leibniz’s Rule: Generalization of the Product Rule for Derivatives


  • 36
  • 0
  • 6.033
  • Reply

  • Open in the desktop app ADD TO PLAYLIST


    Published on Aug 10, 2020
    About :

    In this video I go over Leibniz’s rule which is the generalization of the product rule for derivatives and extends it for all derivatives and not just the first one. I had covered the product rule in my earlier video and showed that the derivative of the product (f·g)’ = f’g + fg’. We can use this same product rule, along with mathematical induction, to prove the general Leibniz rule for the n-th derivative of a product (f·g)(n).

    Leibniz’s rule makes use of the binomial coefficient which I had briefly discussed in a prior video as well. After I prove the rule, I manually derive consecutive derivatives using the product rule, as well as comparing the result with the binomial theorem. I do this to show the amazing synchronicity or similarity between the powers of a binomial (x + y)n and the derivative of a product (f·g)(n).

    The topics covered in this video are listed below with their time stamps.

    • @ 0:42 - Topics to Cover
    1. @ 1:14 - Recap on the Product Rule for Derivatives
    2. @ 2:51 - Leibniz's Rule: Generalization of the Product Rule for Derivatives
      • @ 8:00 - Proof of Leibniz's Rule
      • @ 45:17 - Manually Determining the n-th Derivative Using the Product Rule
      • @ 59:27 - Synchronicity with the Binomial Theorem

    Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIiLYb3IimifHz3HfzeQ?e=rch7UF

    View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/leibniz-general-product-rule-for-derivatives

    Related Videos:

    Derivative Rules - Proof of the Product Rule: http://youtu.be/EIjvGJhDAOk

    Problems Plus Example 4 - Mathematical Induction: http://youtu.be/WdIr_onvUtE

    Infinite Sequences and Series: Representations of Functions as Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-representations-of-functions-as-power-series .

    SUBSCRIBE via EMAIL: https://mes.fm/subscribe

    DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

    Like, Subscribe, Favorite, and Comment Below!

    Follow us on:

    Official Website: https://MES.fm
    Hive: https://peakd.com/@mes
    Gab: https://gab.ai/matheasysolutions
    Minds: https://minds.com/matheasysolutions
    Twitter: https://twitter.com/MathEasySolns
    Facebook: https://fb.com/MathEasySolutions
    LinkedIn: https://mes.fm/linkedin
    Pinterest: https://pinterest.com/MathEasySolns
    Instagram: https://instagram.com/MathEasySolutions
    Email me: contact@mes.fm

    Try our Free Calculators: https://mes.fm/calculators

    BMI Calculator: https://bmicalculator.mes.fm
    Grade Calculator: https://gradecalculator.mes.fm
    Mortgage Calculator: https://mortgagecalculator.mes.fm
    Percentage Calculator: https://percentagecalculator.mes.fm

    Try our Free Online Tools: https://mes.fm/tools

    iPhone and Android Apps: https://mes.fm/mobile-apps

    Tags :

    mathematics calculus science messcience math

    Woo! This creator can upvote comments using 3speak's stake today because they are a top performing creator! Leave a quality comment relating to their content and you could receive an upvote worth at least a dollar.

    Their limit for today is $0!
    Time until mes can give away $0 to their commenters.
    0 Days 0 Hours 0 Minutes 0 Seconds

    To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

    3 views a month ago $
    0 views 2 years ago $

    More Videos

    8 views 2 months ago $
    17 views a year ago $
    8 views a year ago $