Eu pensei que deveria pelo menos concluir com informações matematicamente precisas, não com enrolação do ChatGPT 
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\textcolor{orange}{\hat{r}} & r\hat{\theta} & r\sin\theta\, \hat{\phi} \\
\partial_r & \boxed{\partial_\theta} & \boxed{\partial_\phi} \\
A_r & \boxed{r A_\theta} & \boxed{r\sin\theta\, A_\phi}
\end{matrix} \right|
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\textcolor{orange}{\hat{r}} & r\hat{\theta} & r\sin\theta\, \hat{\phi} \\
\partial_r & \boxed{\partial_\theta} & \boxed{\partial_\phi} \\
A_r & \boxed{r A_\theta} & \boxed{r\sin\theta\, A_\phi}
\end{matrix} \right|
o 1º termo do Rotacional
[center]
\Huge \frac{1}{r^2 \sin\theta} \cdot \textcolor{orange}{\hat{r}}\begin{vmatrix} \partial_\theta & \partial_\phi \\ r A_\theta & r\sin\theta\, A_\phi \end{vmatrix}
[/center]
\textcolor{red}{
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & \textcolor{purple}{r\hat{\theta}} & r\sin\theta\, \hat{\phi} \\
\left.\overrightarrow{\partial_r}\right| & \partial_\theta & \left|\overrightarrow{\;\;\;\;\partial_\phi\;}\right. \\
\left.\underrightarrow{A_r}\right| & r A_\theta & \underrightarrow{\biggl| \, r\sin\theta\, A_\phi \,}
\end{matrix} \right|
}
\textcolor{green}{
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & \textcolor{purple}{r\hat{\theta}} & r\sin\theta\, \hat{\phi} \\
\left|\overrightarrow{\partial_r}\right. & \partial_\theta & \left.\overrightarrow{\;\;\;\;\partial_\phi\;}\right| \\
\left|\underrightarrow{A_r}\right. & r A_\theta & \underrightarrow{ \, r\sin\theta\, A_\phi \, \biggl|}
\end{matrix} \right|
}
o 2º termo do Rotacional
[center]
\Huge \textcolor{red}{- \frac{1}{r^2 \sin\theta} \cdot \textcolor{purple}{r\hat{\theta}}\begin{vmatrix} \partial_\phi & \partial_r \\ r\sin\theta\, A_\phi & A_r \end{vmatrix} }
\Huge \textcolor{green}{+ \frac{1}{r^2 \sin\theta} \cdot \textcolor{purple}{r\hat{\theta}}\begin{vmatrix} \partial_r & \partial_\phi \\ A_r & r\sin\theta\, A_\phi \end{vmatrix} }
[/center]
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & r\hat{\theta} & \textcolor{blue}{r\sin\theta\, \hat{\phi}} \\
\boxed{\partial_r} & \boxed{\partial_\theta} & \partial_\phi \\
\boxed{A_r} & \boxed{r A_\theta} & r\sin\theta\, A_\phi
\end{matrix} \right|
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & r\hat{\theta} & \textcolor{blue}{r\sin\theta\, \hat{\phi}} \\
\boxed{\partial_r} & \boxed{\partial_\theta} & \partial_\phi \\
\boxed{A_r} & \boxed{r A_\theta} & r\sin\theta\, A_\phi
\end{matrix} \right|
o 3º termo do Rotacional
[center]
\Huge \frac{1}{r^2 \sin\theta} \cdot \textcolor{blue}{r\sin\theta\, \hat{\phi}}\begin{vmatrix} \partial_r & \partial_\theta \\ A_r & r A_\theta \end{vmatrix}
[/center]
criei outro Tópico sobre colorir o texto nos títulos dos painéis de detalhes, que poderia corresponder às 3 cores em elementos específicos