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

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bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0\[f(N)= \frac{ RN }{ (1+aN)^b }\]

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0a, b and R are positive constants

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0ok so we get: \[\frac{'( RN) (1+aN)^b  (RN)'(1+aN)^b}{ \left[ (1+aN)^b \right]^2}\]

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0is that it? my book says we also have to use the chain rule but am so confused...

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1you have to use the chain rule to differentiate (1 + aN)^b derivative of this is ab((1 + aN)^(b1)

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0this is the answer: \[\frac{ R }{ (1+aN)^{b+1}}(1abN+aN)\]

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1hold on  i'll check that out on paper

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0ok thank you! :)

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1yea thats right but its a bit messy to set it out  i'll try the draw facility

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0ok, i dnt mind a scan...

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1its not working = R(1 + aN)^b  RNab(a + aN)^(b1)  (1 + aN)^2b = R(1 + aN)^(b1) ( ((1 + aN)  abN)  (1 + aN)^2b = R(1 + aN  abN)  (1 + aN)^(b+1)

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0ok thank you! ^^

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0wait, can i ask a few questions to see if i understand?

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0i dnt understand how you get this, i know you said chain rule? ab(a + aN)^(b1)

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1if 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
 one year ago
Best ResponseYou've already chosen the best response.1thats the chain rule or 'function of a function' rule

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0oh its easier with the Liebniz notation! thank you sooo much! :)

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1the derivative of the 'inside function' (1 + aN) = a and if we let (1 + aN)^b = u^b its derivative is bu^(b1)

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1yep  i find the Leibnitz notation easier for the chain rule

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0my problem is noticing the chain rule because to be the (1+aN)^b didnt look like one :/

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1right maybe its having the lettered constants there intread of actual numbers

bronzegoddess
 one year ago
Best ResponseYou've already chosen the best response.0yes :( i hate applied math, i have an exam tomorrow at 2pm =.=

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1look out for a function within a function

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.1 that was a tricky one and the algebra was a bit bit messy too good luck
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