For $V=V(r)$, where $r^2=x^2_1+x^2_2+...+x^2_n$, $\sum_1^n\frac{∂^2V}{∂x_i^2}=\frac{∂^2V}{∂r^2}+αV_r$, then what is the value of α?

Question

For $V=V(r)$, where $r^2=x^2_1+x^2_2+...+x^2_n$, $\sum_1^n\frac{∂^2V}{∂x_i^2}=\frac{∂^2V}{∂r^2}+αV_r$, then the value of α is

(A)$\frac{1}{r}$

(B)$\frac{n}{r}$

(C)$\frac{(n-1)}{r}$

(D)$0$

I have computed $\frac{∂V}{∂x_i}=\frac{∂V}{∂r}\frac{∂r}{∂x_i}=\frac{∂V}{∂r}\frac{x_i}{\sqrt{\sum_1^n x_i2}}$.

But,from here i got puzzled in calculating second derivative of $V$ w.r.t $x_i$.

I've invested a great amount of time in this problem...I'll be thankful if someone come up with answer