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

If `y=sec^(-1)((x^(2)+1)/(x^(2)-1))`, then find `(dy)/(dx)`.
Here `f^(-1)(x)` expression is of the form `(x^(2)+a^(2))/(x^(2)-a^(2))`, so we substitute `x=tan theta` and then use suitable trigonometrical formula to write it in simplest form and then differentiate

Text Solution

Verified by Experts

The correct Answer is:
`(-2)/(1+x^(2))`
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