For an alternative derivation, we can make use of the usual vector operations to express the total second derivative of the absolute position vector r.
A slice of the graph above showing the function in the xz-plane at y = 1. Note that the two axes are shown here with different scales.
Since acceleration is the time derivative of velocity, the material acceleration can be derived from the definition of material derivative as follows:
Using only direction of vector
UNIT 2: DERIVATIVES
Vector addition for vectors at any angle | Adding vectors | How to add vectors
Vector addition for perpendicular vectors | Adding vectors | How to add vectors
Schematic of a fully connected layer and a matrix multiplication without transfer-function applied.