How would I differentiate this?

I've got a problem similar to this:

( 1+3x ⁄ 1+2x ) ²

(or read as bracket 1+3x over 1+2x bracket squared)

I know you do the quotient rule when you have terms in fractions, but I have no idea what to do since the whole fraction is squared. Any advice?

Reply 1

TenOfThem

Original post by cocoalrose

You have a choice - the straightforward way is to use the chain rule with the quotient rule

Reply 2

cocoalrose

Original post by TenOfThem

You have a choice - the straightforward way is to use the chain rule with the quotient rule

So would I make u = ( 1+3x / 1+2x ) and then y = u² ?

Reply 3

TenOfThem

Original post by cocoalrose

So would I make u = ( 1+3x / 1+2x ) and then y = u² ?

Yes

Reply 4

joeymr

Original post by cocoalrose

So would I make u = ( 1+3x / 1+2x ) and then y = u² ?

I would chain rule the numerator and denominator seperately, thinking of the fraction as (1+3x)^2/(1+2x)^2 to eliminate the all squared. Then apply quotient rule as normal :smile:

Reply 5

TenOfThem

Original post by joeymr

I would chain rule the numerator and denominator seperately, thinking of the fraction as (1+3x)^2/(1+2x)^2 to eliminate the all squared. Then apply quotient rule as normal :smile:

TBH

I would do this too - but either way is fine

Reply 6

cocoalrose

Original post by joeymr

I would chain rule the numerator and denominator seperately, thinking of the fraction as (1+3x)^2/(1+2x)^2 to eliminate the all squared. Then apply quotient rule as normal :smile:

So you can take each of the terms squared? Isn't that different than the entire fraction squared?

Reply 7

joeymr

Original post by cocoalrose

So you can take each of the terms squared? Isn't that different than the entire fraction squared?

Applying a power to a whole fraction is much the same as applying the same power to both the whole of the numerator and the denominator :smile:

(edited 10 years ago)

Reply 8

zNutty

I would be more comfortable with actually multiplying them out then differentiating using the quotient rule. Easy to mess up if you're using the chain rule as well as the quotient rule.

Reply 9

the bear

Original post by cocoalrose

So you can take each of the terms squared? Isn't that different than the entire fraction squared?

no...

(a/b)² is the same as

(a²)/(b²)

Reply 10

TenOfThem

Original post by cocoalrose

So you can take each of the terms squared? Isn't that different than the entire fraction squared?

Oh dear

You really should know the

(\frac{2}{3})^2 = \frac{4}{9}

Reply 11

cocoalrose

Original post by TenOfThem

Oh dear

You really should know the

(\frac{2}{3})^2 = \frac{4}{9}

I obviously understand that, but wasn't sure if that could be done when you are differentiating.

Reply 12

TenOfThem

Original post by cocoalrose

I obviously understand that, but wasn't sure if that could be done when you are differentiating.

I am sorry, but that does not make sense

If you know that a fraction squared is the same as the numerator squared over the denominator squared then you know that they are always the same

Reply 13

cocoalrose

Original post by TenOfThem

I am sorry, but that does not make sense

If you know that a fraction squared is the same as the numerator squared over the denominator squared then you know that they are always the same

I'm sorry that my misunderstanding doesn't make sense to you? I didn't realise you could apply it to differentiation. End of.

Reply 14

TenOfThem

Original post by cocoalrose

I'm sorry that my misunderstanding doesn't make sense to you? I didn't realise you could apply it to differentiation. End of.

I understand you being peed off by my comment

BUT

You need to realise that everything that you already know still holds true - differentiation is just another tool

You, like many students, are overcomplicating something because there is calculus involved - I do not want you to panic and lose your basic algebra skills just because it is a differentiation question

Reply 15

TenOfThem

Original post by cocoalrose

I'm sorry that my misunderstanding doesn't make sense to you? I didn't realise you could apply it to differentiation. End of.

Also, I realise that you are new

Do not let my mean side put you off - I can be mega-helpful too

:biggrin:

Reply 16

davros

Original post by cocoalrose

So you can take each of the terms squared? Isn't that different than the entire fraction squared?

You can rewrite your original function in whatever way you find convenient and then differentiate it - you should not get a different answer!

If you want a simpler example to think of, consider