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 one year ago
ive tried to prove it many times but , i still didnt get it.... if dy/dx = y/x+2y prove that d''y/dx''=8/(x+2y)^3
 one year ago
ive tried to prove it many times but , i still didnt get it.... if dy/dx = y/x+2y prove that d''y/dx''=8/(x+2y)^3

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tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Do you mean \(\dfrac{y}{x+2y}\)? That is NOT what you have written. Folks in calculus should know about the Order of Operations. Have you considered the Quotient Rule for differentiation?

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1really ? sorry i dont know how to write it in the right way...yes i use that quotient rule , but then i got this\[\frac{ \frac{ dy }{ dx }.x+2y(2y.\frac{ dy }{ dx }) }{ (x+2y)^2 }\] then what should i do ?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1You should try that again. The whole numerator is a mess.

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1someby pls help me..i dont get it..... :{

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Numerator: (x+2y)(y')  (y)(1+2y') Look at it very carefully.

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1oh yeahh my numerator is really a mess..then what should i do ?

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1what should i do ~~~~~ omgg

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1even i tried this more than once, and i don't get numerator = 8, is anything else given ?

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1the original question .

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1ohhh...so, xy+y^2 =4.... then its easy, did you get that numerator first ? next thing will be to simplify it.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1got this : (x+2y)(y')  (y)(1+2y') first ?

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1yes i got it just now .haha

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1yes im using that..then quotient rule ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1(x+2y)(y')  (y)(1+2y') is the result of numerator AFTER applying quotient rule, now you have to simplify

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Just for the record, it is ALWAYS more beneficial to show the ORIGINAL problem statement.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yeah, that would have saved me few minutes...

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1to be honest im stucking again

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1what u got after substituting y'=y/(x+2y) in that numerator ?

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1\[2y\frac{ 2y^2 }{ x+2y }\] what about this ? for that numerator

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ 2xy+2y }{ (x+2y)^3 }\]

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1then subtitute (0,2) into that equation ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1its actually this : \(\huge \frac{ 2xy+2y^2 }{ (x+2y)^3 }=\frac{ 2(xy+y^2) }{ (x+2y)^3 }\) now use xy+y^2 =4 and you are done

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(2y\frac{ 2y^2 }{ x+2y }\) was correct

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ 2xy+2y^2}{(x+2y)^3}\]

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1this ????am i right ??

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yeah, factoring out 2 will give you 2 (xy+y^2) and xy+y^2 as per the question is 4

Ika_Kim
 one year ago
Best ResponseYou've already chosen the best response.1ohhhh........i see ur answer........and i totally got it ! thanks a lot @hartnn !!:) really appreciate ^_^
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