Implicit Differentiation Help (1 Viewer)

[RaxX]

Hi, I'm in year 10, so i'm not a genius at this or anything. The question is
(out of Cambridge 3Unit Book)
2e) Find dy/dx for the curves defined by these equations.
e) x^3 + xy^2 = x^2y y^3
my working out is here

Sorry if its a bit messy.
I think i go it wrong, but the answers give an answer by completing the square... so yeah. If you can help me, tell me what i got wrong, that would help a lot. Thanks!

 

[Trebla]

Hi, I'm in year 10, so i'm not a genius at this or anything. The question is
(out of Cambridge 3Unit Book)
2e) Find dy/dx for the curves defined by these equations.
e) x^3 + xy^2 = x^2y y^3
my working out is here

Sorry if its a bit messy.
I think i go it wrong, but the answers give an answer by completing the square... so yeah. If you can help me, tell me what i got wrong, that would help a lot. Thanks!

x³ + xy² = x²y + y³
3x² + y² + 2xy(dy/dx) = 2xy + x²(dy/dx) + 3y²(dy/dx)
dy/dx (2xy - x² - 3y²) = 2xy - 3x² - y²
dy/dx = (2xy - 3x² - y²) / (2xy - x² - 3y²)

Seems fine to me...

 

[RaxX]

so did i do it wrong or right?
thanks for helping.

 

[Dx_God]

wait 1 question, in ur right hand side of the equation, is it + or - between (x^2)y and y^3?

 

[Dx_God]

ur working out is correct but i don't really know if ur first line is wrong or not

 

[RaxX]

its a +

 

[RaxX]

ohno wonder... its supposed to be a -... wtf, i fucked simple arithmetic up.

 

[cutemouse]

I don't think this is 3U stuff to be honest.

 

[RaxX]

whoops, sorry wrong section then. Someone move it. It came out of a 3U textbook im doing for when i start 3U next year lol.

 

[bob fossil]

I did this in 4 unit. Pretty sure you wont see this

 

[The Nomad]

Implicit differentiation isn't in 3U? I always use it in integration by substitution so I'm quite sure it is...

 

[cutemouse]

Implicit differentiation isn't in 3U? I always use it in integration by substitution so I'm quite sure it is...

You don't need to use it though.

Eg. if you use the sub. u^2=x then you can differentiate the 'x', ie. dx/du=2u so dx=2u du.

or if you use implict differentiation, then 2u du/dx =1 so dx=2u du.

 

[RaxX]

really?.... the book says it is 'useful' for 3U

 

[study-freak]

really?.... the book says it is 'useful' for 3U

Well, yeah.
You don't need it, but it's sometimes useful in solving some questions.
It's not a difficult concept so you might as well learn it.

 

[jet]

no question will ever be asked in a 3U paper which required the use of implicit differentiation iirc. the question would be able to be solved through other methods...

This.

really?.... the book says it is 'useful' for 3U

It is, but it's not in the syllabus. It is a much less cogent form of the chain rule which confuses many people.

I taught it to myself in year 9 i think and until I found out it was the chain rule two years later, I had no idea how to use it/how it worked and found it extremely confusing.

 

[Uncle]

never saw implicit differentiation in 3u.

some extra-cirricular bullshit as usual.

should be known by 1st year uni though.