# What is the derivative of arctan(y/x)?

$- \frac{y}{{x}^{2} + {y}^{2}} \frac{\mathrm{dy}}{\mathrm{dx}}$
$\frac{d}{\mathrm{dx}} \arctan \left(\frac{y}{x}\right) = \frac{1}{1 + {\left(\frac{y}{x}\right)}^{2}} \cdot \left(\frac{d}{\mathrm{dx}} \frac{y}{x}\right)$
$\frac{d}{\mathrm{dx}} \arctan \left(\frac{y}{x}\right) = \frac{1}{1 + \left({y}^{2} / {x}^{2}\right)} \cdot \left(- \frac{y}{x} ^ 2 \cdot \frac{\mathrm{dy}}{\mathrm{dx}}\right)$
$\frac{d}{\mathrm{dx}} \arctan \left(\frac{y}{x}\right) = - {x}^{2} / \left({x}^{2} + {y}^{2}\right) \cdot \frac{y}{x} ^ 2 \cdot \frac{\mathrm{dy}}{\mathrm{dx}}$
$\frac{d}{\mathrm{dx}} \arctan \left(\frac{y}{x}\right) = - \frac{y}{{x}^{2} + {y}^{2}} \frac{\mathrm{dy}}{\mathrm{dx}}$