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

Options

A. `(t)/((t^2+2)^2)`
B. `(4t)/((t^2+1)^2)`
C. `(8t)/((t^2+1)^2)`
D. `(4t)/((t^2-1)^2)`

Answer

B

Explanation

We apply the quotient rule with `u=t^2-1` and `v=t^2+1`.
`(dy)/(dt)=(d)/(dt)(u/v)=(v(du//dt)-v(du//dt))/(v^2)`
`=((t^2+1).2t-(t^2-1).2t)/((t^2+1)^2)`
`=(2t^3+2t-2t^3+2t)/((t^2+1)^2)=(4t)/((t^2+1)^2)`