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What is the derivative with respect to $x$ of the function $f(x) = x + x^2 - \ln (x + x^2)$?

$\cfrac{df(x)}{dx} = (1+2x)\left(1 - \cfrac{1}{x+x^2}\right)$

$\cfrac{df(x)}{dx} = 1 + 2x - \cfrac{1}{x+x^2}$

$\cfrac{df(x)}{dx} = 1 + 2x - \cfrac{1}{x} - \cfrac{2x}{x^2}$

$\cfrac{df(x)}{dx} =0$

$\cfrac{df(x)}{dx} = \cfrac{x+x^2}{1+2x}$