# How do you differentiate g(x) =x^2sinx using the product rule?

Dec 24, 2015

The trick is to find the two functions where product rule can be applied. Please go through the explanation for the step by step application of the product rule.

#### Explanation:

The product rule where $u$ and $v$ are functions of $x$

$\left(u v\right) ' = u ' v + v ' u$

The given problem is $g \left(x\right) = {x}^{2} \sin \left(x\right)$

$g \left(x\right) = \left(u v\right)$
$u = {x}^{2}$ and $v = \sin \left(x\right)$

Now to find $u '$ and $v '$

$u = {x}^{2}$
$u ' = 2 x$

$v = \sin \left(x\right)$
$v ' = \cos \left(x\right)$

$g ' \left(x\right) = \left(u v\right) ' = \left(2 x\right) \left(\sin \left(x\right)\right) + {x}^{2} \cos \left(x\right)$

$g ' \left(x\right) = 2 x \sin \left(x\right) + {x}^{2} \cos \left(x\right)$ Answer