# What is the derivative of sin (x/2)?

$\frac{1}{2} \cos \left(\frac{x}{2}\right)$
if you know that $\frac{d}{\mathrm{dx}} \sin x = \cos x$ then you can use the chain rule so by letting $u = \frac{x}{2}$ you have $\frac{d}{\mathrm{du}} \sin u = \cos u$
and $\frac{\mathrm{du}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(\frac{x}{2}\right) = \frac{1}{2}$
$s o \frac{d}{\mathrm{du}} \left(\sin u\right) \setminus \times \frac{\mathrm{du}}{\mathrm{dx}} = \cos u \setminus \times \frac{1}{2} = \frac{1}{2} \cos \left(\frac{x}{2}\right)$