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[tex]\nabla = \sum^3_{i=1} \frac{1}{h_i}\frac{\partial}{\partial q_i}\vec{e}_{q_i}[/tex]

where ##q_i## are generalized coordinates (spherical polar, cylindrical...) and ##h_i## are Lame coefficients. Why then

[tex]div(\vec{A})=\sum^3_{i=1} \frac{1}{h_i}\frac{\partial}{\partial q_i}\vec{e}_{q_i} \cdot \sum_j A_j\vec{e}_{q_j}=\sum_i\frac{1}{h_i}\frac{\partial}{\partial q_i}A_i[/tex]

where I am making the mistake?

here is different definition.

https://www.jfoadi.me.uk/documents/lecture_mathphys2_05.pdf