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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

The correct Answer is:
`(4t)/((t^(2)+1)^(2))`
We apply the Quotient Rule with `u=t^(2)-1andv=t^(2)+1`:
`(d)/(dt)((u)/(v))=(v(du//dt)-(uv//dt))/(v^(2))implies(dy)/(dt)=((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))`
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