I am not sure it is maths or physics question. A stress tensor of a nematic liquid crystal is given as follows
$$ T_{ij}=-P\delta_{ij}-n_{k,i}n_{k,j}+\widetilde{T_{ij}} $$ where $\widetilde{T_{ij}}$ is called the viscous stress and P is the pressure constant as usual. And $n_{k,i}$ is the partial derivative of $k^{th}$ component of director vector $n$ with respective to $x_i$. With observer transformation $$x^{*}=Qx+C$$, where Q is an orthogonal matrix, a vector $A$ is objective if $A^{*}=QA$.
I was asked to show this tensor is objective given that $n$ is objective, i.e $n^{*}=Qn$. I am just not sure how to deal with the partial derivative. Should I use the chain rule? For example $$ n_{k,i}^*=\frac{\partial n_k^*}{\partial x_i^*}=\frac{\partial n_k^*}{\partial X_j}\frac{\partial X_j}{\partial x_i^*} $$ where $X_j$ is a fixed coordinate (Lagrangian). I know $\frac{\partial X_j}{\partial x_i^*}$ is just the inverse of deformation tensor $F$. I don't know what to do next. How should I deal with $\delta_{ij}$? Can anyone help?