Question

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

Answer 1

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

Explanation:

We have

`y(t)=te^t-sint" "=>" "y'(t)=e^t+te^t-cost`

`x(t)=t+e^t" "=>" "x'(t)=1+e^t`

Note the use of the product rule to find `y'(t)`.

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