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Ika_Kim
 2 years 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
Ika_Kim
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1You should try that again. The whole numerator is a mess.

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

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

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

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

hartnn
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1the original question .

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

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

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

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

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

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

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

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

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

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

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

hartnn
 2 years 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
 2 years 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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