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Question
If `y = (1 + 1/x^2)/(1 - 1/x^2)` then `(dy)/(dx)` is ______.
Options
`(-4x)/(x^2 - 1)^2`
`(-4x)/(x^2 - 1)`
`(1 - x^2)/(4x)`
`(4x)/(x^2 - 1)`
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Solution
If `y = (1 + 1/x^2)/(1 - 1/x^2)` then `(dy)/(dx)` is `(-4x)/(x^2 - 1)^2`.
Explanation:
Given `y = (1 + 1/x^2)/(1 - 1/x^2)`
⇒ `y = (x^2 + 1)/(x^2 - 1)`
∴ `(dy)/(dx) = ((x^2 - 1) * 2x - (x^2 + 1) * 2x)/(x^2 - 1)^2`
= `(2x(x^2 - 1 - x^2 - 1))/(x62 - 1)^2`
= `(2x(-2))/(x^2 - 1)^2`
= `(-4x)/(x^2 - 1)^2`
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