# Exactl$$y'$$

Calculus Level 4

$f'(x)+\dfrac{f(x)}{x}-\sqrt{f(x)}=0$

If a function $$f(x)$$ satisfies the above equation and $$f(1)=12$$, then which is of the following is true?

$$A. f(x)=\dfrac{x^3+12x^{\frac{3}{2}}\sqrt{3}-2x^{\frac{3}{2}}-12\sqrt{3}+109}{9x}$$

$$B. f(x)=\dfrac{x^3+12x^{\frac{3}{2}}\sqrt{3}-2x^{\frac{3}{16}}-12\sqrt{3}+109}{9x}$$

$$C.f(x)=\dfrac{x^3+12x^{\frac{5}{2}}\sqrt{3}-2x^{\frac{3}{2}}-12\sqrt{31}+109}{9x}$$

Clarification: $$f'(x)$$ is the first derivative of the function $$f(x)$$.

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