If `y=log{sqrt(x-1)-sqrt(x+1)},` show that `(dy)/(dx)=(-1)/(2sqrt(x^2-1))`

Explanation

`=frac{{d}}{{dx}}(log {sqrt{{x}-1}-sqrt{{x}+1}})`

`=frac{1}{sqrt{{x}-1}-sqrt{{x}+1}} frac{{d}}{{dx}}{sqrt{{x}-1}-sqrt{{x}+1}}`

`=frac{1}{sqrt{{x}-1}-sqrt{{x}+1}} times frac{sqrt{{x}+1}-sqrt{{x}-1}}{2 sqrt{{x}^{2}-1}}`

`=frac{-1}{2 sqrt{x^{2}-1}} quad` [Hence proved `]`