Question

What is the derivative of `f(t) = (t^3e^(1-t) , tan^2t )`?

Answer 1

`(3t^2 e^(1-t) -t^3 e^(1-t))i +2tant sec^2 t j` Or,
`f'(t)= ((3t^2 -t^3)e^(1-t), 2tan t sec^2 t)`

Explanation:

Given f(t) is `t^3 e^(1-t) i + tan^2 t j`

Its derivative f'(t) would be `(3t^2 e^(1-t) -t^3 e^(1-t))i +2tant sec^2 t j`. This can also be expressed as

`f'(t)= ((3t^2 -t^3)e^(1-t), 2tan t sec^2 t)`