Derive the unit vectors ρ, θ, and φ as functions of the
spherical coordinates <ρ, θ, φ> and the Cartesian unit
vectors i, j, and k.
1. Suppose that ρ, θ, and φ depend on time t. Compute dρ/dt ,
dθ/dt , and dφ/dt , leaving results in terms of the spherical
coordinates and the Cartesian unit vectors.
2. Express the derivatives dρ/dt , dθ/dt , and dφ/dt in terms of
the spherical coordinates and spherical unit vectors.
3. Compute...