If $\frac{d}{d x}\left\{\left(\frac{x-1}{x-\sqrt{x}}\right) e^{2 x+1}\right\}=\frac{x-1}{x-\sqrt{x}} e^{2 x+1} f(x)$, then $f(4)=$

• A

  $0$
• B

  $1$
• C

  $\frac{35}{24}$
• Correct answer
  D

  $\frac{47}{24}$

Hence, the correct answer is option: 'D'.