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Below is the solution:

n(2x+y) = x +1 

Differentiate both sides, using the Chain Rule on the left side. 
(1 / (2x + y)) d(2x + y)/dx = 1 
(1 / (2x + y)) (2 + dy/dx) = 1 

Rearrange to isolate dy/dx. 

carlos2112

Answer:

\(\frac{dy}{dx} =\frac{1}{x}\)

Step-by-step explanation:

Given:

\(ln(2xy)\)

We need to find the derivate respect to x, so using the chain rule:

\(\frac{dy}{dx} (ln(2xy))=\frac{dln(u)}{du}\frac{du}{dx}\)

where:

\(u=2xy\)

and:

\(\frac{d}{du} log(u)=\frac{1}{u}\)

so:

\(=\frac{d}{dx}(2xy)\frac{1}{2xy}=2y(\frac{d}{dx}x)\frac{1}{2xy} =\frac{2y}{2xy}\)

Simplifying the expression

\(\frac{2y}{2xy}=\frac{1}{x}\)

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