Friday, 13 January 2017

`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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