# How do you use the product rule to find the derivative of y=x^2*sin(x) ?

Mar 23, 2018

$y ' = x \left(2 \sin x + x \cos x\right)$

#### Explanation:

The Product Rule tells us that if we have two functions $f \left(x\right) , g \left(x\right) ,$ multiplied by one another, then

$\left(f g\right) ' = f g ' + g f '$

Here, for $y = {x}^{2} \sin x ,$ we see $f \left(x\right) = {x}^{2} , g \left(x\right) = \sin x$

Thus,

$y ' = \sin x \frac{d}{\mathrm{dx}} {x}^{2} + {x}^{2} \frac{d}{\mathrm{dx}} \sin x$

$y ' = 2 x \sin x + {x}^{2} \cos x$

Factor out $x$ to simplify:

$y ' = x \left(2 \sin x + x \cos x\right)$