Question

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

Answer 1

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

Explanation:

Take the derivative component-by-component:

`f(t) = (t^2+1, t-e^(1-t))`

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

`= (2t, 1-e^(1-t)(-1))` (don't forget the chain rule!)

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