Question

Question #2c4f7

Answer 1

ans. the derivative is `(-e^(-2y))/(x-1)^2`, where `y =ln sqrt((x+1)/(x-1))`.

Explanation:

see, at first let `y =ln sqrt((x+1)/(x-1))`
or `e^y = sqrt((x+1)/(x-1))`
or `e^(2y)` =`(x+1)/(x-1)` (sqaring)
now differenting the above w.r.t x we get ,
`dy/dx 2e^(2Y)`=`((x-1)-(x+1))/(x-1)^2` by `(d(u/v)/dx) method`
or `dy/dx e^(2y)` =`-1/(x-1)^2`
or we get `dy/dx =-e^(-2y)/(x-1)^2` where `y=lnsqrt((x+1)/(x-1))`.