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))
Krizalid is correct. but in my experience, logarithmic differentiation is done this way:
$\displaystyle y = \sqrt{(x - 1)(x - 2)(x - 3)} = [(x - 1)(x - 2)(x - 3)]^{\frac 12}$
take the log of both sides
$\displaystyle \Rightarrow \ln y = \ln [(x - 1)(x - 2)(x - 3)]^{\frac 12}$
$\displaystyle \Rightarrow \ln y = \frac 12 \left[ \ln (x - 1) + \ln (x - 2) + \ln (x - 3) \right]$
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