# How do you find the derivative of sin^2(x/6)?

Nov 12, 2016

$\frac{1}{6} \sin \left(\frac{x}{3}\right)$

#### Explanation:

Diffrentiate the power first, followed by trigonometry and finally the index.

$\frac{d}{\mathrm{dx}} \left({\sin}^{2} \left(\frac{x}{6}\right)\right)$
$= \left[2 \sin \left(\frac{x}{6}\right) \cos \left(\frac{x}{6}\right)\right] \left(\frac{1}{6}\right)$
$= \frac{1}{6} \sin \left(\frac{x}{3}\right)$

since sin2x = 2 sinxcosx