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Find the derivative of y=(t^2-1)/(t^2+1)...

Find the derivative of `y=(t^2-1)/(t^2+1)`.

Text Solution

Verified by Experts

We apply the Quotient Rule with `u = t^2 - 1` and `v = t^2 + 1`
`(dy)/(dt) = ((t^2 + 1)2t-(t^2 -1)2t)/((t^2 + 1)^(2))`
`["As "d/(dt) (u/v) = (v (du//dt)-u(dv//dt))/(v^2)]`
`=(2t^3 + 2t - 2t^3 + 2t)/((t^2 + 1)^(2)) = (4t)/((t^2 + 1)^(2))`
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