# How do you find the derivative of s=tsint?

Mar 6, 2017

$s ' \left(t\right) = \sin t + t \cos t$

#### Explanation:

This will require the product rule for derivatives.

Recall that the product rule states that given a function that is the product of two other functions,

$s \left(t\right) = f \left(t\right) \cdot g \left(t\right)$

its derivative is

$s ' \left(t\right) = f ' \left(t\right) \cdot g \left(t\right) + f \left(t\right) \cdot g ' \left(t\right)$

For this expression,

$f \left(t\right) = t$
and
$g \left(t\right) = \sin t$

So,

$s ' \left(t\right) = \left(1\right) \cdot \sin t + t \cdot \cos t$

$s ' \left(t\right) = \sin t + t \cos t$