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Christos
 3 years ago
Double Implicit differantion,
So I got this:
http://screencast.com/t/HZNKpdBC
Now I have found that dy/dx = 2x/3y
How can I find d^2y/dx^2
?
Christos
 3 years ago
Double Implicit differantion, So I got this: http://screencast.com/t/HZNKpdBC Now I have found that dy/dx = 2x/3y How can I find d^2y/dx^2 ?

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Christos
 3 years ago
Best ResponseYou've already chosen the best response.0@hero @jim @Luigi0210 @EsaaLoca @eSpeX @Emily778 @timo86m @zzr0ck3r

eSpeX
 3 years ago
Best ResponseYou've already chosen the best response.1If \[\frac{dy}{dx}=\frac{2x}{3y}\]Then you just need to take the partial derivative of that to get the 2nd derivative.

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0I solved this now I am trying to solve this: http://screencast.com/t/tlp6QrmBh7 Here is the solution: But my result is: (2y^3x+2x^4)/y^5

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0Solution: http://screencast.com/t/ZKI6Di9vkR8j ***

eSpeX
 3 years ago
Best ResponseYou've already chosen the best response.1Take your solution and factor an x out to get theirs.

eSpeX
 3 years ago
Best ResponseYou've already chosen the best response.1Okay, so this is what you have so far, right?\[x^{3}+y^{3}=1\rightarrow 3x^{2}+3y^{2}\frac{dy}{dx}=0\rightarrow \frac{dy}{dx}=\frac{3x^{2}}{3y^{2}}\rightarrow \frac{dy}{dx}=\frac{x^{2}}{y^{2}}\]

eSpeX
 3 years ago
Best ResponseYou've already chosen the best response.1Then you take the derivative of that using the quotient rule of \[[\frac{f(x)}{g(x)}]'=\frac{g(x)f(x)'f(x)g(x)'}{[g(x)]^{2}}\] which is \[\frac{y^2(2x)x^2(2y)\frac{dy}{dx}}{[y^{2}]^{2}}\]

Christos
 3 years ago
Best ResponseYou've already chosen the best response.0It's ok guys I think am gonna surpass this, I guess my answer is similar enought if not 100% correct , am gonna do some derivatives and head to sleep

eSpeX
 3 years ago
Best ResponseYou've already chosen the best response.1Seems I get the same answer you did, not sure where they are getting that extra x.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[2x^{2}3y ^{2}=4\] \[2*2x3*2y \frac{ dy }{dx }=0\] \[2x3y \frac{ dy }{dx }=0,\frac{ dy }{dx }=\frac{ 2x }{ 3y }\] \[\frac{ d ^{2}y }{dx ^{2} }=\frac{ 2 }{3 }\frac{y*1x \frac{ dy }{dx } }{ y ^{2} }\] \[\frac{ d ^{2}y }{dx ^{2} }=\frac{ 2 }{3 }\frac{yx \frac{ 2x }{3y } }{y ^{2} }\] \[\frac{ d ^{2}y}{dx ^{2} }=\frac{ 2 }{ 3 }\frac{ \frac{ 3y ^{2}2x ^{2} }{ 3y } }{y ^{2} }\] \[\frac{ d ^{2}y }{ dx ^{2} }=\frac{ 2 }{9 }\frac{ 2x ^{2}3y ^{2} }{ y ^{3} }\] \[\frac{ d ^{2}y }{ dx ^{2} }=\frac{ 2 }{9 }\frac{ 4 }{y ^{3} }\] \[\frac{ d ^{2}y }{dx ^{2} }=\frac{ 8 }{9y ^{3} }\]
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