Let $f$ be a differentiable function with $\lim _{x \rightarrow \infty} f(x)=0 .$ If $y^{\prime}+y f^{\prime}(x)-f(x) f^{\prime}(x)=0, \lim _{x \rightarrow \infty} y(x)=0$, then $\left(\right.$ where $\left.y^{\prime}=\frac{d y}{d x}\right)$

• A

  $y+1=e^{f(x)}+f(x)$
• B

  $y-1=e^{f(x)}+f(x)$
• Correct answer
  C

  $y+1=e^{-f(x)}+f(x)$
• D

  $y-1=e^{-f f] x}+f(x)$

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