differentiate the following, I am stuck so I really don't know what to do..

- anonymous

differentiate the following, I am stuck so I really don't know what to do..

- katieb

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- anonymous

\[f(N)= \frac{ RN }{ (1+aN)^b }\]

- anonymous

a, b and R are positive constants

- cwrw238

use the quotient rule

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## More answers

- anonymous

ok so we get:
\[\frac{'( RN) (1+aN)^b - (RN)'(1+aN)^b}{ \left[ (1+aN)^b \right]^2}\]

- anonymous

is that it? my book says we also have to use the chain rule but am so confused...

- cwrw238

you have to use the chain rule to differentiate (1 + aN)^b
derivative of this is ab((1 + aN)^(b-1)

- anonymous

this is the answer:
\[\frac{ R }{ (1+aN)^{b+1}}(1-abN+aN)\]

- cwrw238

hold on - i'll check that out on paper

- anonymous

ok thank you! :)

- cwrw238

yea thats right but its a bit messy to set it out
- i'll try the draw facility

- anonymous

ok, i dnt mind a scan...

- cwrw238

its not working
= R(1 + aN)^b - RNab(a + aN)^(b-1)
-------------------------------
(1 + aN)^2b
= R(1 + aN)^(b-1) ( ((1 + aN) - abN)
-----------------------------
(1 + aN)^2b
= R(1 + aN - abN)
---------------
(1 + aN)^(b+1)

- anonymous

ok thank you! ^^

- cwrw238

yw

- anonymous

wait, can i ask a few questions to see if i understand?

- cwrw238

yes OK

- anonymous

i dnt understand how you get this, i know you said chain rule?
ab(a + aN)^(b-1)

- cwrw238

if we have a function of a function like (1 + 2x)^3
the derivative of this is found this way:
(using the dy/dx notation):
let u = 1 + 2x , then y = u^3 so dy/du = 3u^2
and du/dx = 2
so dy/dx = dy/du * du/dx = 2 * 3 u^2 = 6 u^2 = 6(1 + 2x)^2
you can use the notation f'(x) to show the same thing but personally i prefer the 'd' notation.
ithe differentiation in your question can be done similarly

- cwrw238

thats the chain rule or 'function of a function' rule

- anonymous

oh its easier with the Liebniz notation! thank you sooo much! :)

- cwrw238

the derivative of the 'inside function' (1 + aN) = a
and if we let (1 + aN)^b = u^b its derivative is bu^(b-1)

- cwrw238

yep - i find the Leibnitz notation easier for the chain rule

- anonymous

my problem is noticing the chain rule because to be the (1+aN)^b didnt look like one :/

- cwrw238

right maybe its having the lettered constants there intread of actual numbers

- anonymous

yes :( i hate applied math, i have an exam tomorrow at 2pm =.=

- cwrw238

look out for a function within a function

- anonymous

i will :)

- cwrw238

- that was a tricky one and the algebra was a bit bit messy too
good luck

- anonymous

thank you!^^

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