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Find the derivative of $f(x)=\dfrac{x^3}{x+3x^2}$.

A

$\dfrac{3x^2}{1+6x}$

B

$\dfrac{3x^2+2x}{9x^4+6x^3+x^2}$

C

$\dfrac{3x^2+2x}{9x^2+6x+1}$

D

$\dfrac{9x^2+2x}{3x^2+6x+1}$

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