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Math Help - Implicit & Exponential Differentiation

  1. #1
    Newbie richard_c's Avatar
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    Implicit & Exponential Differentiation

    Can anyone tell me how I have done with these ones on Implicit & Exponential Differentiation?
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    Super Member Aryth's Avatar
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    a)

    x^2 + y^2 - 2x - 6y + 5 = 0

    Now we differentiate it implicitly:

    2x + 2yy' - 2 - 6y' = 0

    2yy' - 6y' = -2x + 2

    y'(2y - 6) = 2x + 2

    y' = \frac{2x + 2}{2y - 6}

    b)

    x^2 + 2xy + 3y^2 = 4

    Implicitly:

    2x + (2y + 2xy') + 6yy' = 0

    2x + 2y + 2xy' + 6yy' = 0

    2xy' + 6yy' = -2x - 2y

    y'(2x + 6y) = -2x - 2y

    y' = \frac{-x - y}{x + 3y}

    With this you are forgetting that when you differentiate y in terms of x then you must do something along the lines of:

    \frac{dy}{dx}[y^2] = 2y\frac{dy}{dx}

    =2yy'
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