ind its tangent function,
    \(C'(t)\).
  </p>
    <p>
    In the absence of the requisite discipline and mathematical wit, 
    one approach to calculating the X-spline tangent function is
    to brute force the result via computational methods.
    This approach also has the benefit of directly 
    producing output in the form
    of R code that can be evaluated and, because the X-spline equation
    is piecewise, it efficiently replicates across multiple equations.
  </p>
    <p>
    The first step is 