Posted by **Michelle** on Friday, May 4, 2012 at 8:27am.

How do I differentiate

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

and the second differentiate it?

HELP ASAP is much appreciated

- Calculus -
**Bosnian**, Friday, May 4, 2012 at 10:19am
Go on:

wolframalpha dot com

When page be open in rectangle type:

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

and click option =

After a few seconds , when you see result click option:

Show steps

- Calculus -
**Bosnian**, Friday, May 4, 2012 at 10:47am
second derivative is derivative of first derivative

on wolframalpha dot com type :

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

and click option =

then

Show steps

- Calculus -
**Reiny**, Friday, May 4, 2012 at 10:52am
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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