$A$ particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = \beta x^{-2n}$,where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by:

• A
  $-2n \beta^2 x^{-2n-1}$
• B
  $-2n \beta^2 x^{-4n-1}$
• C
  $-2n \beta^2 x^{-2n+1}$
• D
  $-2n \beta^2 x^{-4n+1}$