`y = ln sqrt((x + 1)/(x - 1)))` Find the derivative of the function.

`y=lnsqrt[(x+1)/(x-1)]`

`y=ln(x+1)^(1/2)-ln(x-1)^(1/2)`

`y=1/2ln(x+1)-1/2ln(x-1)`

` ` `y'=1/[2(x+1)]-1/[2(x-1)]`

`y'=[(x-1)-(x+1)]/[2(x+1)(x-1)]`

`y'=[x-1-x-1]/[2(x+1)(x-1)]`

`y'=-1/[(x+1)(x-1)]`

The derivative of the function y is `-1/[(x+1)(x-1)].`

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`y=lnsqrt[(x+1)/(x-1)]`

`y=ln(x+1)^(1/2)-ln(x-1)^(1/2)`

`y=1/2ln(x+1)-1/2ln(x-1)`

` ` `y'=1/[2(x+1)]-1/[2(x-1)]`

`y'=[(x-1)-(x+1)]/[2(x+1)(x-1)]`

`y'=[x-1-x-1]/[2(x+1)(x-1)]`

`y'=-1/[(x+1)(x-1)]`

The derivative of the function y is `-1/[(x+1)(x-1)].`

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