# How do you use implicit differentiation to find (dy)/(dx) given x^3+y^3=1?

Jan 10, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {x}^{2} / {y}^{2}$

#### Explanation:

Differentiate the equation with respect to $x$:

$\frac{d}{\mathrm{dx}} \left({x}^{3} + {y}^{3}\right) = \frac{d}{\mathrm{dx}} 1$

$3 {x}^{2} + 3 {y}^{2} \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {x}^{2} / {y}^{2}$