# How do you differentiate given sin^2(x/6)?

Jun 16, 2016

$\frac{\mathrm{df}}{\mathrm{dx}} = \sin \left(\frac{x}{3}\right)$

#### Explanation:

As $f \left(x\right) = {\sin}^{2} \left(\frac{x}{6}\right)$

Using chain rule, $\frac{\mathrm{df}}{\mathrm{dx}} = 2 \sin \left(\frac{x}{6}\right) \times \cos \left(\frac{x}{6}\right)$

Now as $2 \sin A \cos A = \sin 2 A$,

$\frac{\mathrm{df}}{\mathrm{dx}} = \sin \left(\frac{x}{3}\right)$