# What is the derivative of (-sinx^2)/2?

May 29, 2017

$\frac{d}{\mathrm{dx}} \left(- \sin {x}^{2} / 2\right) = - x \cos {x}^{2}$

#### Explanation:

Using the chain rule with $u = {x}^{2}$:

$\frac{d}{\mathrm{dx}} \left(- \sin {x}^{2} / 2\right) = - \frac{1}{2} \frac{d}{\mathrm{du}} \left(\sin u\right) \times \frac{\mathrm{du}}{\mathrm{dx}}$

$\frac{d}{\mathrm{dx}} \left(- \sin {x}^{2} / 2\right) = - \frac{1}{2} \cos {x}^{2} \times \frac{{\mathrm{dx}}^{2}}{\mathrm{dx}}$

$\frac{d}{\mathrm{dx}} \left(- \sin {x}^{2} / 2\right) = - \frac{1}{2} \cos {x}^{2} \times 2 x$

$\frac{d}{\mathrm{dx}} \left(- \sin {x}^{2} / 2\right) = - x \cos {x}^{2}$