What is the Parametric Differentiation Method for Repeated Quotient Rule?

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Discussion Overview

The discussion revolves around the parametric differentiation method, particularly in the context of applying the repeated quotient rule for taking multiple derivatives of certain functions. Participants explore techniques and resources related to this method, including references to calculus tricks and specific examples.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant recalls a technique from Calculus I for simplifying the process of taking multiple derivatives that involves the repeated use of the quotient rule.
  • Another participant suggests that the method may relate to using the difference of squares to transform a function into a product, which could then be differentiated using the product or quotient rule.
  • A different participant elaborates on the idea of reducing the numerator while increasing the power of the denominator, mentioning a factorial pattern associated with this method.
  • A participant references a math methods book that describes a method for differentiating constants, suggesting it may relate to the parametric differentiation technique discussed.

Areas of Agreement / Disagreement

Participants express various ideas and techniques related to the topic, but there is no clear consensus on a single method or approach. Multiple viewpoints and interpretations of the parametric differentiation method are presented.

Contextual Notes

Some participants reference external resources and examples, but the discussion does not resolve the specifics of the parametric differentiation method or its applications. There are indications of different interpretations and techniques without a unified understanding.

Who May Find This Useful

This discussion may be of interest to students and educators in calculus, particularly those exploring advanced differentiation techniques or seeking alternative methods for handling repeated derivatives.

Skyler0114
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Hi Guys,
I remember back in the days of Calc I learning that there was an easy way to take multiple derivatives of certain functions that needed repeated uses of the quotient rule. I was wondering if anybody remembered that trick.
 
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is this like using the difference of squares to reduce the function into a product of factors that you then can use the product or quotient rule on:

http://calculustricks.com/page/3/
 
jedishrfu said:
is this like using the difference of squares to reduce the function into a product of factors that you then can use the product or quotient rule on:

http://calculustricks.com/page/3/
It involved the denominator and easily reducing something in the numerator instead of having to do all the distributing and addition to then reduce. Instead of squaring the denominator everytime you only increased it's power by one. Also it has a factorial pattern in there if i recall correctly.
Like here:

http://www.wolframalpha.com/input/?i=derivative+arctan(x)&lk=4&num=1
http://www.wolframalpha.com/input/?i=+2nd+derivative+arctan(x)
http://www.wolframalpha.com/input/?i=+3rd+derivative+arctan(x)
http://www.wolframalpha.com/input/?i=4th+derivative+arctan(x)
http://www.wolframalpha.com/input/?i=5th+derivative+arctan(x)

and another function
http://www.wolframalpha.com/input/?i=derivative+1/(x+1)
http://www.wolframalpha.com/input/?i=2nd+derivative+1/(x+1)
http://www.wolframalpha.com/input/?i=3rd+derivative+1/(x+1)
http://www.wolframalpha.com/input/?i=3rd+derivative+x%2F%28x^3%2B1%29
 

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