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Spherical Polar Coordinates

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I am trying to find the grad function of the spherical polar coordinates shown on the attached file. I have completed the question to a certain extent but am not sure if it is correct. Could you please ensure its accuracy and complete by simplifying the solution (trig identities etc) as I am unable to do so?

(See attached file for full problem description)

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Solution Summary

The spherical polar coordinates are examined.

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