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

##### 1 Answer
Apr 21, 2016

$f ' \left(t\right) = \left(1 + {e}^{t} , {e}^{t} + t {e}^{t} - \cos t\right)$

#### Explanation:

We have

$y \left(t\right) = t {e}^{t} - \sin t \text{ "=>" } y ' \left(t\right) = {e}^{t} + t {e}^{t} - \cos t$

$x \left(t\right) = t + {e}^{t} \text{ "=>" } x ' \left(t\right) = 1 + {e}^{t}$

Note the use of the product rule to find $y ' \left(t\right)$.

$f ' \left(t\right) = \left(1 + {e}^{t} , {e}^{t} + t {e}^{t} - \cos t\right)$