logarithmic differentiation
posted by ana .
y= 4th root (x^2+1)/(x^21)

y = [(x^2 + 1)(x^21) ]^(1/4)
= (x^4  1)^(1/4)
ln y = (1/4) ln(x^4 1)
(dy/dx) / y = (1/4)(4x^3)/(x^4  1)
dy/dx = (1/4)(y)(4x^3)/(x^4  1)
or
you can replace y with (x^4  1)^(1/4)
and simplify that a bit since the denominator is x^4  1 
Do you want the derivative of that? Does the "fourth root" apply to the numerator only, or the complete fraction
(x^2+1)/(x^21) ?
You need to write the function in a clear nonambiguous manner, using parentheses where necessary. Use ^1/4 for fourth roots. 
Sorry ana, my answer is incorrect,
I read that as a multiplication , should have been a division
ln y = (1/4) (ln (x^2 + 1)  ln(x^2 1)
(dy/dx) / y = (1/4) ( 2x/(x^2+1)  2x/(x^2 + 1) )
dy/dx = (1/4)(y) (4x)/(x^4  1)
= xy/(x^4  1)
replace y with the original if you have to.