The gradient of a scalar field like gravity potential in spherical coordinates is a matter of standard mathematical definition involving radial and angular partial derivatives, so no citation is needed.
The claim states a fundamental vector calculus identity concerning the gradient operator in spherical coordinates, which naturally breaks down into radial and angular components (derivatives with respect to radius, polar angle, and azimuthal angle). This is a textbook mathematical definition taught in introductory physics and calculus, making it common knowledge.