1.

if `y=(1+1/x^(2))/(1-1/(x)^(2))`,then `(dy)/(dx)` is equal toA. `(-4x)/(x^(2)-1)^(2)`B. `(-4x)/(x^(2)-1)`C. `(1-x^(2))/(4x)`D. `(4x)/(x^(2)-1)`

Answer» Correct Answer - a
Given, `y=(1+1/x^(2))/(1-1/x^(2)) rArr y=(x^(2)+1)/(x^(2)-1)`
`therefore (dy)/(dx) = ((x^(2)-1)2x-(x^(2)+1)(2x))/((x^(2)-1)^(2))` [by quotient rule]
`(dy)/(dx) = (2x(x^(2)-1-x^(2)-1))/(x^(2)-1)^(2)`
`=(2x(-2))/(x^(2)-1)^(2)=(-4x)/(x^(2)-1)^(2)`


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