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 (2y10) = 4x + 12
dy/dx = (4x + 12)/(2y10) = (2x6)/(5y)
d(dy)/(dx)^2 = ( (5y)(2)  (2x6)(dy/dx) )/(5y)^2
I then substituted dy/dx with (2x6)/(5y) and got
( 2(5y)^2  (2x6)^2 )/(5y)^3
you could expand that but it would look messier.