Verify the following relations by 

(i) graphical construction of vectors and the parallelogram law and 

(ii) by transforming the vectors to Cartesian coordinates and then taking the derivatives:

\[\begin{aligned}\frac{\partial}{\partial \theta}\left(e_{\theta}\right) & =-e_{r} \\\frac{\partial}{\partial \theta}\left(e_{r}\right) & =e_{\theta}\end{aligned}\]

What would the corresponding relations in spherical coordinates be?