I am working in 2D space. This is a problem related to computing bond force vector from energy density.
The bond energy density, w = $\frac{1}{2} \overrightarrow{\eta} \cdot \mathbf{C} \cdot \overrightarrow{\eta}$, where C = $\frac{1}{\xi} \left[ c(\overrightarrow{n} \otimes \overrightarrow{n}) + k(\mathbf{I} - \overrightarrow{n} \otimes \overrightarrow{n}) \right]$. c and $\kappa$ are constants.
$\overrightarrow{n}$ is a unit vector of $(\overrightarrow{\eta} + \overrightarrow{\xi})$.
$\overrightarrow{\xi}$ and $\overrightarrow{\eta}$ are the initial relative position vectors between two particles and displacement vectors after displacement respectively.
The author has written the value for $\frac{dw}{d\eta} = \mathbf{C} \cdot \overrightarrow{\eta}$.
The question i am having is that when you are differentiating w w.r.t $\overrightarrow{\eta}$, the term C contains elements of $\overrightarrow{\eta}$. And I believe this also should be differentiated.
But, the way the result was presented seems to disregard this. Am I missing something?