Let $\mathrm{\varphi }\left(x\right)$ be the inverse of the function $f\left(x\right)$ and $f^{\prime }\left(x\right)=\frac{1}{1+x^5}$, then $\frac{d}{dx}\varphi \left(x\right)$ is equal to

• A

  $\frac{1}{1+{\left[\mathrm{\varphi }\left(x\right)\right]}^5}$
• B

  $\frac{1}{1+{\left[f\left(x\right)\right]}^5}$
• Correct answer
  C

  $1+{\left[\mathrm{\varphi }\left(x\right)\right]}^5$
• D

  $1+f\left(x\right)$

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