Quotient Rule - is this right or wrong?

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Discussion Overview

The discussion revolves around the application of the quotient rule and chain rule in calculus, specifically regarding the differentiation of functions expressed as quotients and powers. Participants explore different methods for approaching these problems and consider their effectiveness and commonality in practice.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests rearranging the function to apply the quotient rule directly, questioning the acceptability of this method.
  • Another participant agrees that the alternate method is acceptable.
  • Some participants argue that using the chain rule is preferable, as it may reduce tedious algebra and ensure correct application.
  • A participant expresses a preference for their own method but acknowledges the potential benefits of the chain rule approach.
  • There is a question about which method is more commonly practiced, indicating uncertainty about standard approaches in calculus.
  • A later reply reflects a realization that the chain rule method is more logical and efficient, indicating a shift in understanding.

Areas of Agreement / Disagreement

Participants express differing opinions on the preferred method for differentiation, with some advocating for the chain rule while others find merit in their own rearrangement approach. The discussion does not reach a consensus on which method is superior.

Contextual Notes

Participants note that their preferences may depend on familiarity with the methods and that there is no universally "more logical" approach. The discussion highlights the subjective nature of learning calculus and the exploration of different techniques.

Who May Find This Useful

This discussion may be useful for calculus students, particularly those self-studying, who are exploring different methods for differentiation and seeking to understand the implications of their choices.

singleton
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Quotient Rule -- is this right or wrong?

Well the book I'm learning from suggests you take the following:

y = ( (2x + 3) / (x + 4) ) ^ 2

And use the chain rule first.

However, the way I find easiest is to re-arrange it so that:
y = (2x + 3) ^ 2 / (x + 4) ^ 2

That way I can go straight to the quotient rule although it is a little bit more cluttered (just more inside the brackets).

Is my way acceptable?

I am doing the same thing for sqrt( (3 - x) / (3 + x) )

Instead of doing it the way my book suggests I re-arrange it to:
sqrt(3 - x) / sqrt(3 + x)
And then once again I rearrange it to:
(3 - x) ^ 1/2 / (3 + x) ^ 1/2
 
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Is my way acceptable?

Yes, of course.
 
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In the problems posed above, you should probably think of your alternate methods as a check that you are applying the chain rule correctly.

In my opinion, one should not avoid the chain rule.
By avoiding the chain rule, you force yourself to endure some repetitive and unnecessarily tedious algebra.

For example, it's probably best to use the chain rule for y=(x+1)^5.
 
robphy said:
In the problems posed above, you should probably think of your alternate methods as a check that you are applying the chain rule correctly.

In my opinion, one should not avoid the chain rule.
By avoiding the chain rule, you force yourself to endure some repetitive and unnecessarily tedious algebra.

For example, it's probably best to use the chain rule for y=(x+1)^5.

Ok good idea. I'll do one way and then use the other as a check.

I do use the chain rule for things like y=(x+1)^5

It is just that (for some reason) I felt more comfortable with the way I was doing it.

The only other question I have is which was is more common--the way my book suggests doing it or the method I do it?

If its a common "practice" to use the book's way then I'll do that.
 
Erm well I re-read my book and it turns out that the "chain rule first" method is not only more logical but it saves me time and like the other posted said some repetitive and tedious algebra heh.

/sorry

I'm a newbie to calculus and teaching it to myself :(
 
singleton said:
Erm well I re-read my book and it turns out that the "chain rule first" method is not only more logical but it saves me time and like the other posted said some repetitive and tedious algebra heh.

/sorry

I'm a newbie to calculus and teaching it to myself :(
Take your time and try and find your preferred way, there is no "more logical" way but yes once your used to methods some of them save you time.
 

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