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Econometrics

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Derivative of a Natural Log

EMETRC-YNVEXT

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

A

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

B

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

C

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

D

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

E

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