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I usually think of a gradient as being a property of a single-variable function... but anyway, is this what you want?

sage: F.diff()
[(r, phi, theta) |--> -1/r^2      (r, phi, theta) |--> 0      (r, phi, theta) |--> 0]
[     (r, phi, theta) |--> 0      (r, phi, theta) |--> 0      (r, phi, theta) |--> 0]
[     (r, phi, theta) |--> 0      (r, phi, theta) |--> 0      (r, phi, theta) |--> 0]
sage: diff(F)
[(r, phi, theta) |--> -1/r^2      (r, phi, theta) |--> 0      (r, phi, theta) |--> 0]
[     (r, phi, theta) |--> 0      (r, phi, theta) |--> 0      (r, phi, theta) |--> 0]
[     (r, phi, theta) |--> 0      (r, phi, theta) |--> 0      (r, phi, theta) |--> 0]