## bronzegoddess 2 years ago differentiate the following, I am stuck so I really don't know what to do..

1. bronzegoddess

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

2. bronzegoddess

a, b and R are positive constants

3. cwrw238

use the quotient rule

4. bronzegoddess

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

5. bronzegoddess

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

6. cwrw238

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

7. bronzegoddess

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

8. cwrw238

hold on - i'll check that out on paper

9. bronzegoddess

ok thank you! :)

10. cwrw238

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

11. bronzegoddess

ok, i dnt mind a scan...

12. 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)

13. bronzegoddess

ok thank you! ^^

14. cwrw238

yw

15. bronzegoddess

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

16. cwrw238

yes OK

17. bronzegoddess

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

18. 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

19. cwrw238

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

20. bronzegoddess

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

21. 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)

22. cwrw238

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

23. bronzegoddess

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

24. cwrw238

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

25. bronzegoddess

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

26. cwrw238

look out for a function within a function

27. bronzegoddess

i will :)

28. cwrw238

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

29. bronzegoddess

thank you!^^

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