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If y = log ((1-x^(2))/(1+x^(2))), then...

If ` y = log ((1-x^(2))/(1+x^(2)))`, then `(dy)/(dx)` is equal to

A

` (4x^(3))/(1-x^(4))`

B

`(-4x)/(1-x^(4))`

C

` (1)/(4-x^(4))`

D

`(-4x^(3))/(1-x^(4))`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `y = log((1-x^(2))/(1+x^(2)))`
`:. (d y)/(dx) = (1)/((1-x^(2))/(1+x^(2))).(d)/(dx)((1-x^(2))/(1+x^(2)))`
`= ((1+x^(2)))/((1-x^(2))).((1+x^(2)).(-2x)-(1-x^(2)).2x)/((1+x^(2))^(2))`
`= (-2x[1+x^(2)+1-x^(2)])/((1-x^(2)).(1+x^(2))) = (-4x)/(1-x^(4))`
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