Proof of Quotient Rule using Product Rule

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Discussion Overview

The discussion revolves around the derivation of the quotient rule in calculus, specifically how it can be understood through the application of the product rule. Participants are exploring the steps involved in this derivation and clarifying a particular transition between steps.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant seeks clarification on the derivation of the quotient rule as presented on Wikipedia, expressing confusion about a specific transition between steps.
  • Another participant suggests that the confusion arises from multiplying by ##1 = \frac{h(x)}{h(x)}## to facilitate the derivation.
  • A third participant acknowledges the simplicity of the explanation provided and expresses gratitude for the clarification.
  • A moderator notes the relocation of the thread to a more appropriate section, emphasizing the technical nature of the question.
  • The moderator also provides a guideline regarding image size for future posts.

Areas of Agreement / Disagreement

Participants generally agree on the method of multiplying by 1 in the form of h(x) over itself as a key step in the derivation, but the initial participant's confusion indicates that not all aspects of the derivation are fully resolved.

Contextual Notes

The discussion does not address potential limitations or assumptions in the derivation process, nor does it resolve any uncertainties regarding the steps involved.

gomess
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Hey guys, just trying to understand how the quotient rule is derived, so I head over to wikipedia and saw this:

attachment.php?attachmentid=68783&stc=1&d=1397845277.jpg


But I'm having some difficulty understanding what goes on between these two steps:

attachment.php?attachmentid=68784&stc=1&d=1397845277.jpg


Could someone shed some light on this?
 

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It looks like they are multiplying by ##1 = \frac{h(x)}{h(x)}##
 
Oh, okay. Cant believe I didnt see that; it was so simple. Sorry to whoever moved my thread for posting in wrong the section. Thanks Zondrina!
 
I moved it. This seemed more like a technical question than homework, so I move it here.

Also, what Zondrina said is exactly what happened - they multiplied by 1 in the form of h(x) over itself.

Also, if you post images again, crop or shrink them so that they fit. 900 pixels wide is about the maximum - yours is 1071 pixels wide, so causes the post to be too wide.
 
Alright, no problem. Thanks again guys.
 

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