I need to find dx/dy using logarithmetic differentiation. Thanks for any help!!

1. y = sqrt((x-1) (x-2) (x-3))

2. y= sqrt((x^2-2)/(x^2+2))

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- Nov 3rd 2007, 12:53 PMSMAlvarezlogarithmetic differentiation
I need to find dx/dy using logarithmetic differentiation. Thanks for any help!!

1. y = sqrt((x-1) (x-2) (x-3))

2. y= sqrt((x^2-2)/(x^2+2)) - Nov 3rd 2007, 02:33 PMKrizalid
Shouldn't it be

Now take the derivative. - Nov 3rd 2007, 02:39 PMJhevon
Krizalid is correct. but in my experience, logarithmic differentiation is done this way:

take the log of both sides

Now differentiate implicitly.

of course Krizalid's method is equivalent, the difference is, you do not have to differentiate implicitly with his method, explicit differentiation works - Nov 3rd 2007, 04:14 PMSMAlvarez
so is the final answer :

1/2[(1/x-1)+(1/x-2)+(1/x-3)]

?

How would I start the second one? - Nov 3rd 2007, 04:17 PMJhevon