# How do find the derivative of y = x^2 sinx?

Aug 5, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x \sin \left(x\right) + {x}^{2} \cos \left(x\right)$

#### Explanation:

You can use the product rule to find the derivative. The product rule says the following:

If $h \left(x\right) = f \left(x\right) g \left(x\right)$, then $h ' \left(x\right) = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$

In our case,

$h \left(x\right) = {x}^{2} \sin x$

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

$g \left(x\right) = \sin x$

$f ' \left(x\right) = 2 x$

$g ' \left(x\right) = \cos x$

Plug in those values into our definition for the product rule to get

$\frac{\mathrm{dy}}{\mathrm{dx}} = h ' \left(x\right) = 2 x \sin \left(x\right) + {x}^{2} \cos \left(x\right)$