Quotient Rule - is this right or wrong?

[singleton]

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

 

[Muzza]

Is my way acceptable?

Yes, of course.

 

[robphy]

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.

 

[singleton]

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.

 

[singleton]

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 :(

 

[Zurtex]

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.