Posted by **ana** on Monday, May 14, 2012 at 4:15pm.

y= 4th root (x^2+1)/(x^2-1)

- logarithmic differentiation -
**Reiny**, Monday, May 14, 2012 at 4:27pm
y = [(x^2 + 1)(x^2-1) ]^(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

- logarithmic differentiation -
**drwls**, Monday, May 14, 2012 at 4:29pm
Do you want the derivative of that? Does the "fourth root" apply to the numerator only, or the complete fraction

(x^2+1)/(x^2-1) ?

You need to write the function in a clear nonambiguous manner, using parentheses where necessary. Use ^1/4 for fourth roots.

- missed the division sign - logarithmic differentiation -
**Reiny**, Monday, May 14, 2012 at 4:45pm
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.

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