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Calculus

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How do I differentiate
ln (2X^2 - 12X + Y^2 -10Y)

and the second differentiate it?

HELP ASAP is much appreciated

  • Calculus -

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    derivative ln (2X^2 - 12X + Y^2 -10Y)

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  • Calculus -

    second derivative is derivative of first derivative

    on wolframalpha dot com type :

    derivative 4 ( x - 3 ) / [ 2 x ^ 2 - 12 x + ( y -10 ) y ]

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  • Calculus -

    If this were
    2x^2 - 12x + y^2 - 10y = 0
    it would be an ellipse and we could do something with it
    I will assume that much
    secondly I will assume you want dy/dx

    4x - 12 + 2y dy/dx - 10dy/dx = 0
    dy/dx (2y-10) = -4x + 12
    dy/dx = (-4x + 12)/(2y-10) = (2x-6)/(5-y)

    d(dy)/(dx)^2 = ( (5-y)(2) - (2x-6)(-dy/dx) )/(5-y)^2

    I then substituted dy/dx with (2x-6)/(5-y) and got

    ( 2(5-y)^2 - (2x-6)^2 )/(5-y)^3

    you could expand that but it would look messier.

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