Question

use logarithmic differentiation to do: y=(x^2 +1/x^2 -1)^1/4

Answer 1

\[y=(\frac{ x ^{2}+1 }{ x^{2}-1 })^{\frac{ 1 }{ 4 }}\]

Answer 2

\[\ln(y)=\frac{1}{4}\left(\ln(x^2+1)-\ln(x^2-1)\right)\] is a start

Answer 3

could you walk me through it?

Answer 4

then take the derivative piece by piece
leave the \(\frac{1}{4}\) out front

Answer 5

the derivative of \(\ln(f(x))\) is \(\frac{f'(x)}{f(x)}\) so the next step would be to take the derivative of \(\ln(y)\) and get
\[\frac{1}{4}\left(\frac{2x}{x^2+1}-\frac{2x}{x^2-1}\right)\]

Answer 6

then to finish, multiply by the original function

Answer 7

thanks