Φ[r_, θ_, ϕ_] := {r Sin[θ] Cos[ϕ], r Sin[θ] Sin[ϕ], r Cos[θ]}
grad = Grad[f@Φ[r, θ, ϕ], {r, θ, ϕ}]
TeXForm @ Style[grad, TextAlignment -> Left]
$\scriptsize\left\{\cos (\theta ) f^{(\{0,0,1\})}(\{r \sin (\theta ) \cos (\phi ),r \sin (\theta ) \sin (\phi ),r
\cos (\theta )\})+\\ \ \ \ \sin (\theta ) \sin (\phi ) f^{(\{0,1,0\})}(\{r \sin (\theta ) \cos (\phi ),r
\sin (\theta ) \sin (\phi ),r \cos (\theta )\})+\\ \ \ \ \sin (\theta ) \cos (\phi ) f^{(\{1,0,0\})}(\{r
\sin (\theta ) \cos (\phi ),r \sin (\theta ) \sin (\phi ),r \cos (\theta )\}),\\ -r \sin (\theta )
f^{(\{0,0,1\})}(\{r \sin (\theta ) \cos (\phi ),r \sin (\theta ) \sin (\phi ),r \cos (\theta
)\})+\\ \ \ \ r \cos (\theta ) \sin (\phi ) f^{(\{0,1,0\})}(\{r \sin (\theta ) \cos (\phi ),r \sin (\theta
) \sin (\phi ),r \cos (\theta )\})+\\ \ \ \ r \cos (\theta ) \cos (\phi ) f^{(\{1,0,0\})}(\{r \sin (\theta
) \cos (\phi ),r \sin (\theta ) \sin (\phi ),r \cos (\theta )\}),\\r \sin (\theta ) \cos (\phi )
f^{(\{0,1,0\})}(\{r \sin (\theta ) \cos (\phi ),r \sin (\theta ) \sin (\phi ),r \cos (\theta
)\})-\\ \ \ \ r \sin (\theta ) \sin (\phi ) f^{(\{1,0,0\})}(\{r \sin (\theta ) \cos (\phi ),r \sin (\theta
) \sin (\phi ),r \cos (\theta )\})\right\}$
Grad[f@\[CapitalPhi][r, \[Theta], \[Phi]], {r, \[Theta], \[Phi]}]
? $\endgroup$