# Product rule

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The product rule is a rule of differentiation which states that for a differentiable function $uv$:

$\frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}$

In prime notation:

$(uv)'=uv'+vu'$

In the case of three terms multiplied together, the rule becomes

$\frac{d}{dx}(uvw)=uw\frac{dv}{dx}+vw\frac{du}{dx}+uv\frac{dw}{dx}$

One of the most common differentiation rules used for functions of combination, it is also very simple to apply. For instance, consider the function $f(x)=x\sin(x)$ . The derivative is easily found:

$f'(x)=x\frac{d}{dx}(\sin(x))+\sin(x)\frac{d}{dx}(x)$
$f'(x)=x\cos(x)+\sin(x)$