Question

How do you differentiate `s=(t^2+1)/(1-t^2)`?

Answer 1

Use the quotient rule.

Explanation:

`(ds)/dt = ((2t)(1-t^2)-(t^2+1)(-2t))/(1-t^2)^2`

Now use algebra to simplify.

`= (2t-2t^3+2t(t^2+1))/(1-t^2)^2`

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