In this blog post, the author explains how to find the second and higher order derivatives of a transform, building on their previous discussion about the relationship between derivatives, logarithms, and transforms. The key concept is that the second derivative of a transform can be found by multiplying the first derivative by (log(T) * log(T)). This simple approach can be extended to find the nth derivative, with the formula (x^{n}(t) = log(T)^n * x(t)). The author provides an interactive example where users can visualize the tangent vector and acceleration vector of a point as it is interpolated using the transform.
https://nosferalatu.com/HigherOrderDerivativesTransforms.html