# How do you find dy/dx by implicit differentiation given x^3+y^3=2?

Jan 4, 2017

I differentiate each term separately, reassemble the equation, and then solve for $\frac{\mathrm{dy}}{\mathrm{dx}}$

#### Explanation:

Differentiate the first term:

$\frac{d \left({x}^{3}\right)}{\mathrm{dx}} = 3 {x}^{2}$

Differentiate the second term:

$\frac{d \left({y}^{3}\right)}{\mathrm{dx}} = 3 {y}^{2} \frac{\mathrm{dy}}{\mathrm{dx}}$

Differentiate the third term:

$\frac{d \left(2\right)}{\mathrm{dx}} = 0$

Reassemble the equation:

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

Solve for $\frac{\mathrm{dy}}{\mathrm{dx}}$:

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

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