How do you implicitly differentiate  x^2 + 4y^2 = 36?

$\frac{d}{\mathrm{dx}} \left({x}^{2} + 4 {y}^{2}\right) = \frac{d}{\mathrm{dx}} \left(36\right) \implies 2 x + 4 \cdot 2 y \cdot \frac{\mathrm{dy}}{\mathrm{dx}} = 0 \implies \frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{x}{4 y}$