# How do you find the derivative of f(x) = 2x(sinx)cos(x)?

Nov 2, 2016

The answer is $= \sin 2 x + 2 x \cos 2 x$

#### Explanation:

Use $2 \sin x \cos x = \sin 2 x$
$\therefore f \left(x\right) = x \sin 2 x$
We use the product rule to find the derivative
$\left(u v\right) ' = u ' v + u v '$
$u = x$$\implies$$u ' = 1$
$v = \sin 2 x$$\implies$$v ' = 2 \cos 2 x$
so, $f ' \left(x\right) = \sin 2 x + 2 x \cos 2 x$
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