# How do you differentiate f(x)= 7xsin2x using the product rule?

Oct 24, 2016

$f ' \left(x\right) = 7 \sin x + 14 x \cos 2 x$

#### Explanation:

The product rule of derivatives is:
$\textcolor{b l u e}{\left(u \left(x\right) \cdot v \left(x\right)\right) ' = u ' \left(x\right) \cdot v \left(x\right) + v ' \left(x\right) \cdot u \left(x\right)}$

$f ' \left(x\right) = 7 \left(x \sin 2 x\right) '$

$f ' \left(x\right) = 7 \cdot \left(\textcolor{b l u e}{x ' \sin x + x \left(\sin 2 x\right) '}\right)$
f'(x)=7*(1*sinx+x(2cos2x)
$f ' \left(x\right) = 7 \cdot \left(\sin x + 2 x \cos 2 x\right)$
$f ' \left(x\right) = 7 \sin x + 14 x \cos 2 x$