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

Derive the function y^2=x+ln(y/x) with respect to x

Answer

$0=\frac{-1}{x}+1$

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

$0=\frac{-1}{x}+1$

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

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

0.29 seconds