Question

Derivations of gradient, divergence and curl in spherical coordinate system full
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Answer 1

For most general approach ,study the orthogonal curvilinear coordinate system. The expressions for gradient, divergence and curl in this coordinate system are available in many books on theoretical ( mathematical) physics. For example see M.L Boas's book .Even, Griffiths has given the expressions in his book of classical electrodynamics. From those expressions , by making substitution of parameters ( base or scale factors)for various coordinate systems( available in tabular form) we can get the required expressions for grad. div. and curl in any orthogonal coordinate system. There are 11 such systems.These systems are given in Introduction to quantum machinists by Pauling and Wilson. This is an old book.