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# Find the derivative of x^2y+xy^3*3=(1-1x)/x

### Formulas

$\frac{d}{dx}\left(3y^3x+y\cdot x^2\right)=\frac{x\frac{d}{dx}\left(1-x\right)-\left(1-x\right)}{x^2}$

## Step-by-step explanation

Problem

$\frac{d}{dx}\left(x^2y+3x y^3=\frac{1-x}{x}\right)$
1

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

$\frac{d}{dx}\left(3y^3x+y\cdot x^2\right)=\frac{d}{dx}\left(\frac{1-x}{x}\right)$

$\frac{d}{dx}\left(3y^3x+y\cdot x^2\right)=\frac{x\frac{d}{dx}\left(1-x\right)-\left(1-x\right)}{x^2}$
$\frac{d}{dx}\left(x^2y+3x y^3=\frac{1-x}{x}\right)$

### Main topic:

Differential calculus

0.3 seconds