For a two-dimensional plane, the unit vectors, $\left(\hat{e}_r, \hat{e}_\theta\right)$ of the polar coordinate system and $(\hat{\imath}, \hat{\jmath})$ of the cartesian coordinate system, are related by the following two equations.
$$
\begin{aligned}
& \hat{e}_r=\cos \theta \hat{\imath}+\sin \theta \hat{\jmath} \\
& \hat{e}_\theta=-\sin \theta \hat{\imath}+\cos \theta \hat{\jmath}
\end{aligned}
$$
Which one of the following is the $\text{CORRECT}$ value of $\frac{\partial\left(\hat{e}_r+\hat{e}_\theta\right)}{\partial \theta}$ ?
- $1$
- $\hat{e}_{\theta}$
- $\hat{e}_{r}+\hat{e}_{\theta}$
- $-\hat{e}_{r}+\hat{e}_{\theta}$