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.
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
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 .
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