The higher derivatives of the inverse tangent function and rapidly   convergent BBP-type formulas
  We give a closed formula for the $n^{th}$ derivative of $\arctan x$. A new expansion for $\arctan x$ is also obtained and rapidly convergent series for $\pi$ and $\pi\sqrt 3$ are derived. 
Kunle Adegoke and Olawanle Layeni
math.NT