Question

What is the derivative of `f(t) = (t/(t+2) , t/(t^2-1) )`?

Answer 1

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

Explanation:

We have to keep this in parametric form, so we use the quotient rule and find
`d/dt(f(t)) = (d/dt(t/(t+2)), d/dt(t/(t^2-1)) )`
`= (((t+2)*1 - t*1)/((t+2)^2), ( (t^2-1) - t * (2t) )/((t^2-1)^2))`
`= ((2)/(t+2)^2, -(t^2+1)/(t^2-1)^2)`

our final answer.