Calculating electric field

Could someone explain how to complete this problem?

The electric potential is
V(r,θ) = C1 /r + C2 cosθ /r2
where (r, θ, φ) are the spherical polar coordinates in three dimensions.
[ Data: C1 = 3.2 V m ; C2 = 1.0 V m2 .]


(A) Calculate the electric field at point A: (x, y, z) = (R, 0, 0) on the x axis; R = 1 m. (Give the Cartesian components (Ex, Ey, Ez).)

(B) Calculate the electric field at point B: (x, y, z) = (0, 0, R) on the z axis.

Use the del operator:

(A) E = - del (V)
del operator in the spherical coordinates system is:
E = -1 * [ dV/dr + <θ> 1/r dV/dθ + <φ> 1/ (r sinθ) dV/dφ]
Here , <θ>, and <φ> are unit vectors along the r, θ, and φ direction, respectively.
dV/dr = -C1/r^2 - 2C2 cosθ / r^3
dV/dθ = -C2 sin θ / r^2
dV/dφ = 0

So E = C1/r^2 + 2C2 cosθ / r^3 + <θ> C2 sin θ / r^3

(x,y,z) = (1, 0, 0)
So r = 1, θ = pi/2, and φ = 0.
Therefore, E = C1 + <θ> C2
Now you need some vector conversion

= sin θ cos φ + cos θ cos φ <θ> - sin φ <φ>
= sin θ sin φ + cos θ sin φ <θ> + cos φ <φ>
= cos θ - sin θ <θ>

so given θ and φ,
Ex = Er = C1 = 3.2 V/m
Ey = 0
Ez = - Eθ = -C2 = -1.0 V/m

E = C1 - C2 = 3.2 V/m - 1.0 V/m

Ans: -1.0 V/m

(B) This time (x,y,z) = (0, 0, R)
So r = 1, θ = 0, and φ = Not applicable.
E = C1/r^2 + 2C2 cosθ / r^3 + <θ> C2 sin θ / r^3
E = C1 + 2C2

Again, vector conversions:

= sin θ cos φ + cos θ cos φ <θ> - sin φ <φ>
= sin θ sin φ + cos θ sin φ <θ> + cos φ <φ>
= cos θ - sin θ <θ>

so given θ and φ,
Ex = 0
Ey = 0
Ez = Er = C1 + 2C2 = 3.2 + 2 = 5.2 V/m

Ans: 5.2 V/m