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

Derive the function y+xy^3*3+x^2=(1-1x)/x with respect to x

Answer

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

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Differential calculus

Used formulas:

6. See formulas

Time to solve it:

~ 0.58 seconds