What is the formula for gradient?

Assume you want to know what is the formula of the gradient of the function in multivariable calculus.

Let F be a scalar field function in n-dimension. Then, the gradient of a function is:

∇F = <fx1 , fx2, ... , fxn>

In the 3-dimensional Cartesian space:

∇F = <fx, fy, fz>