# How do you find the derivative of f(t) = t^2sin t?

Mar 2, 2018

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

#### Explanation:

For this problem we must use a rule called the product rule:

$\frac{d}{\mathrm{dt}} \left(h \left(t\right) g \left(t\right)\right) = h ' \left(t\right) g \left(t\right) + h \left(t\right) g ' \left(t\right)$

Where $h ' \left(t\right) = \frac{d}{\mathrm{dt}} \left(h \left(t\right)\right)$ if your not aware

So in this $h \left(t\right) = {t}^{2}$ and $g \left(t\right) = \sin t$

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

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