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

Nov 5, 2015

$- 2 x \sin \left(x\right) + 2 \cos \left(x\right)$

#### Explanation:

Use the product rule: $\left(u v\right) ' = u \cdot v ' + v \cdot u '$
in this case $u = 2 x$ and $v = \cos \left(x\right)$
So...
$\left(u v\right) ' = u \cdot v ' + v \cdot u '$
$\left(u v\right) ' = 2 x \cdot \left(\cos \left(x\right)\right) ' + \cos \left(x\right) \cdot \left(2 x\right) '$

the derivative of $\cos \left(x\right)$ is $- \sin \left(x\right)$

$\left(u v\right) ' = - 2 x \sin \left(x\right) + 2 \cos \left(x\right)$