# Help with the derivation of a variant of Coulomb's Law

My E&M textbook says the following: The electric field at position $$r= (x,y,z)$$ generated by a point charge $$q$$ at the origin is given by $$\vec{E}(r) =\frac{q}{4π\epsilon_0r^2}\hat r=\frac{q}{4π\epsilon_0}\frac{x\hat i+y\hat j+z\hat k}{(x^2+y^2+z^2)^{\frac{3}{2}}}$$ I understand Coulomb's Law, but how is the right side of the equation derived?

The electric field generated by a point charge is radial, which means the $$\hat{i}$$ on the left should actually be: $$$$\hat{r}=\frac{\vec{r}}{r}=\frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{x^2+y^2+z^2}}$$$$