# What is the derivative of cos(x^2)?

Set $u = {x}^{2}$ hence apply chain rule to get
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(\frac{\mathrm{dy}}{\mathrm{du}}\right) \cdot \frac{\mathrm{du}}{\mathrm{dx}} = - \sin u \cdot \left(2 x\right) = - 2 x \cdot \sin \left({x}^{2}\right)$