Question

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

and the second differentiate it?

HELP ASAP is much appreciated

Answer 1

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:

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Answer 2

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

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Answer 3

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.