# How do you find dy/dx by implicit differentiation given x^4+y^4=5?

Dec 20, 2016

The answer is $= - {x}^{3} {\left(5 - {x}^{4}\right)}^{- \frac{3}{4}}$

#### Explanation:

Let's do the differentiation

${x}^{4} + {y}^{4} = 5$

$4 {x}^{3} + 4 {y}^{3} \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 4 {x}^{3}}{4 {y}^{3}}$

$= - {x}^{3} / {y}^{3}$

But, ${y}^{4} = 5 - {x}^{4}$

${y}^{3} = {\left(5 - {x}^{4}\right)}^{\frac{3}{4}}$

Therefore,

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {x}^{3} / {\left(5 - {x}^{4}\right)}^{\frac{3}{4}} = - {x}^{3} {\left(5 - {x}^{4}\right)}^{- \frac{3}{4}}$