Question

Find derivative

Answer 1

\[\ln \frac{ x+1 }{ \sqrt{x-1} }\]

Answer 2

\[\ln(x+1)-\ln(\sqrt{x-1}\]

Answer 3

\[\frac{ 1 }{ x+1 }*1- \frac{ 1 }{ \sqrt{x-1} }*\frac{ 1 }{ 2\sqrt{x} }\]

Answer 4

the first term is ok, the second term is ln (x -1)^1/2 = 1/2 ln (x-1) , then take derivative from here. don't forget add the first term

Answer 5

so the 2nd term would be
\[\frac{ 1 }{ 2\sqrt{x-1} }*\frac{ 1 }{ 2\sqrt{x} }\]

Answer 6

\[\ln \frac{ x+1 }{ \sqrt{x-1} }\\ln(x+1)-\ln(\sqrt{x-1}\\ln(x+1)-\frac{1}{2}ln(x-1)\]take derivative
\[\frac{1}{x+1}-\frac{1}{2}*\frac{1}{x-1}\]simplify them.

Answer 7

Oh I see. I kept the sqrt on x-1 and forgot to separate from 1/2

Answer 8

ok