Consider the function $f^{\prime \prime}(x)=\sec ^4 x+4$ with $f(0)=0$ and $f^{\prime}(0)=0$. What is $f^{\prime}(x)$ equal to?

• A

  $\tan x-\frac{\tan ^3 x}{3}+4 x$
• Correct answer
  B

  $\tan x+\frac{\tan ^3 x}{3}+4 x$
• C

  $\tan x+\frac{\sec ^3 x}{3}+4 x$
• D

  $-\tan x-\frac{\tan ^3 x}{3}+4 x$

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