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    Okay im just practising some questions and the question is,

    If  x^2 + y^2 = 2y find dy/dx in terms of x and y

    okay for this part i did:

    2x + 2y. dy/dx =  2. dy/dx

    dy/dx(2y - 2)= -2x

    dy/dx = x/(1-y)

    then this is the part im stuck on:

    Show that d^2y/dx^2 = 1/(1-y)^3

    i tried using quotient rule however i put everything in terms of x to make it easier to differentiate but that becomes nasty and no where near the answer, i did this by re arranging the first eq to make x the subject:

    x= (2y-y^2)^1/2

    then subbed this into the x/ (1-y) then proceeded with the quotient rule and ended up getting:

    1/(2y-y^2)^ 1/2 + (2y-y^2)^ 1/2 / (1-y)^2

    i then tried using product rule by changing the first differential into x(1-y)^-1 and got closer...

    i got:

    x(1-y) + (1-y)^2 / (1-y)^3

    So yeahhh... someone show me what im doing wrong...
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    Might look into where you made your error if I'm still awake in a little bit, but I would advise just differentiating x/(1-y) implicitly. You can then replace any dy/dx s with the formula you got for that. Seems simpler to me.
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    (Original post by Slumpy)
    Might look into where you made your error if I'm still awake in a little bit, but I would advise just differentiating x/(1-y) implicitly. You can then replace any dy/dx s with the formula you got for that. Seems simpler to me.
    hmm okay ill try this now
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    (Original post by a10)
    hmm okay ill try this now
    Your error is when you do the second differentiation. Have a look at your result, and think about why it might be wrong (the one where you use the quotient rule). Without your workings for the product rule, I don't know what you've done (although my suspicion is a similar mistake).
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    (Original post by Slumpy)
    Your error is when you do the second differentiation. Have a look at your result, and think about why it might be wrong (the one where you use the quotient rule). Without your workings for the product rule, I don't know what you've done (although my suspicion is a similar mistake).
    fudge i forgot to differentiate implicitly :facepalm:

    okay thanks ill try thiis
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    (Original post by Slumpy)
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    thank you, i solved it now
 
 
 

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