Question

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

Answer 1

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

Answer 2

a, b and R are positive constants

Answer 3

use the quotient rule

Answer 4

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

Answer 5

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

Answer 6

you have to use the chain rule to differentiate (1 + aN)^b

derivative of this is ab((1 + aN)^(b-1)

Answer 7

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

Answer 8

hold on - i'll check that out on paper

Answer 9

ok thank you! :)

Answer 10

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

Answer 11

ok, i dnt mind a scan...

Answer 12

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)

Answer 13

ok thank you! ^^

Answer 14

yw

Answer 15

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

Answer 16

yes OK

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

look out for a function within a function

Answer 27

i will :)

Answer 28

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

good luck

Answer 29

thank you!^^