## bronzegoddess Group Title differentiate the following, I am stuck so I really don't know what to do.. one year ago one year ago

1. bronzegoddess Group Title

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

2. bronzegoddess Group Title

a, b and R are positive constants

3. cwrw238 Group Title

use the quotient rule

4. bronzegoddess Group Title

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

5. bronzegoddess Group Title

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

6. cwrw238 Group Title

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

7. bronzegoddess Group Title

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

8. cwrw238 Group Title

hold on - i'll check that out on paper

9. bronzegoddess Group Title

ok thank you! :)

10. cwrw238 Group Title

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

11. bronzegoddess Group Title

ok, i dnt mind a scan...

12. cwrw238 Group Title

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)

13. bronzegoddess Group Title

ok thank you! ^^

14. cwrw238 Group Title

yw

15. bronzegoddess Group Title

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

16. cwrw238 Group Title

yes OK

17. bronzegoddess Group Title

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

18. cwrw238 Group Title

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

19. cwrw238 Group Title

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

20. bronzegoddess Group Title

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

21. cwrw238 Group Title

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

22. cwrw238 Group Title

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

23. bronzegoddess Group Title

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

24. cwrw238 Group Title

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

25. bronzegoddess Group Title

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

26. cwrw238 Group Title

look out for a function within a function

27. bronzegoddess Group Title

i will :)

28. cwrw238 Group Title

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

29. bronzegoddess Group Title

thank you!^^