Question

How do you find the derivative of `((t^(2)+1)/(t^(2)-1))`?

Answer 1

`f'(t) = (-4t)/(t^2-1)^2`

Explanation:

`f(t) = ((t^2+1)/(t^2-1))`

`f'(t) = ((t^2-1) (2t) - (t^2+1)(2t))/(t^2-1)^2` (Quotient rule)

`= (2t(t^2-1-t^2-1))/(t^2-1)^2`

`= (-4t)/(t^2-1)^2`