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DLS
 3 years ago
If "this" is true,then prove that (x^2y^2+3)dy/dx=1
DLS
 3 years ago
If "this" is true,then prove that (x^2y^2+3)dy/dx=1

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Kelumptus
 3 years ago
Best ResponseYou've already chosen the best response.0is that x+1/n+1/x+1/x to infinity?

Kelumptus
 3 years ago
Best ResponseYou've already chosen the best response.0I see what you mean but now that I understand the question I would have to say that I am not sure either :/. Hopefully someone more knowledgeable than myself looks at this...

DLS
 3 years ago
Best ResponseYou've already chosen the best response.0Here's the printed question,just if its not clear

DLS
 3 years ago
Best ResponseYou've already chosen the best response.0If "this" is true,then prove that (x^2y^2+3)dy/dx=1

DLS
 3 years ago
Best ResponseYou've already chosen the best response.0To prove: \[(x^{2}y^{2}+3)\frac{dy}{dx}=1\]

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.1use this \[Y=X+\frac{ 1 }{ Y }\]

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2the given equation \[\large y=x+\frac{ 1 }{ x+\frac{ 1 }{ x+... } }\] is equivalent to \[\large y=x+\frac{ 1 }{ y }\]

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2find the derivative by implicit differentiation

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.1also you can substitute x at the place where you have to prove a desired result

DLS
 3 years ago
Best ResponseYou've already chosen the best response.0please ellaborate,I'm doing this type of question first time

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2\[\large y = x+\frac{ 1 }{ \left[ x+\frac{ 1 }{ x+... } \right] }=x+\frac{ 1 }{ y }\] because the bracketed expression is equal to y

Kelumptus
 3 years ago
Best ResponseYou've already chosen the best response.0Ahh, that's clever sirm3d, makes sense now. I couldn't figure this one out.

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2just take the derivative of both sides by implicit differentiation. the derivative of the LHS is \[\large (dy/dx)\] the derivative of the RHS is 1 

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.1LHS  left hand side RHS right hand side

Kelumptus
 3 years ago
Best ResponseYou've already chosen the best response.0Here is a good reference for implicit differentiation: http://www.intmath.com/differentiation/8derivativeimplicitfunction.php

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2oops, the derivative of the RHS is \[\large 1  \frac{ 1 }{ y^2 }(dy/dx)\]

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.1@DLS i guess you can do it now

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2\[\large \frac{ 1 }{ y }=y^{1}\]

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.1he differentiated it , implicitly

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ dy (x^n) }{ dx }=nx^{n1}\]

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2by power rule and chain rule, the derivative of y^(1) is \[1y^{2} \frac{ dy }{ dx }\]

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2equate the derivative of the LHS to the derivative of the RHS, then group terms with (dy/dx)
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