<center> [![](https://img.3speakcontent.online/ybaefwxz/post.png)](https://3speak.online/watch?v=mes/ybaefwxz) ▶️ [Watch on 3Speak](https://3speak.online/watch?v=mes/ybaefwxz) </center> --- 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)<sup>(n)</sup>. 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)<sup>n</sup> and the derivative of a product (f·g)<sup>(n)</sup>. 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](http://youtu.be/EIjvGJhDAOk) Problems Plus Example 4 - Mathematical Induction: [http://youtu.be/WdIr_onvUtE](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 --- ▶️ [3Speak](https://3speak.online/watch?v=mes/ybaefwxz)
author | mes | ||||||
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category | hive-181335 | ||||||
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In this video I expand upon the product rule for derivatives, which was for just 1 derivative, and show that it can be generalized to the n-th derivative and which is called the general Leibniz rule. View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/leibniz-general-product-rule-for-derivatives
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