If $y=|\cos x-\sin x|+|\tan x-\cot x|$, then $\left(\frac{d y}{d x}\right)_{x=\frac{\pi}{3}}+\left(\frac{d y}{d x}\right)_{x=\frac{\pi}{6}}=$

• A

  1
• B

  -1
• C

  2
• Correct answer
  D

  0

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