# How do you find the derivative of f(t) = t² sin t?

May 9, 2017

$f ' \left(t\right) = {t}^{2} \cos t + 2 t \sin t$

#### Explanation:

$f \left(t\right) = {t}^{2} \sin t$

The Product rule states that:

If $f \left(t\right) = g \left(t\right) h \left(t\right)$ then $f ' \left(t\right) = g \left(t\right) h ' \left(t\right) + g ' \left(t\right) h \left(t\right)$

In this example: $g \left(t\right) = {t}^{2}$ and $h \left(t\right) = \sin t$

Hence, $f ' \left(t\right) = {t}^{2} \cdot \frac{d}{\mathrm{dt}} \sin t + \frac{d}{\mathrm{dt}} {t}^{2} \cdot \sin t$

$= {t}^{2} \cos t + 2 t \sin t$