# Derive the function x^3y+y^3x=30 with respect to x

## Answer

$y^3+3y\cdot x^{2}=0$

## Step-by-step explanation

Problem

$\frac{d}{dx}\left(x^3y+y^3x=30\right)$

1

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(x\cdot y^3+y\cdot x^3\right)=\frac{d}{dx}\left(30\right)$

## Answer

$y^3+3y\cdot x^{2}=0$