Can anybody teach me how to take the gradient of something?

I'm trying to do physics and they have the formlua


gradient of Electromagnetic field = 0


and gradient of magnetic field = 0





what exactly is a gradient?Can anybody teach me how to take the gradient of something?
A gradient requires taking the partial derivatives with respect to each variable. For example, if your function is f(x,y) = x^2 + 2xy +y^3, the partial of x is 2x +2y and the partial of y is 2x +3y^2. The gradient is then (2x+2y) * unit vector of x + (2x+3y^2) * unit vector of y, usually (2x+2y)i + (2x+2y^2)j.Can anybody teach me how to take the gradient of something?
Technically speaking operator of gradient is defined as





grad = e_i ∂/∂x_i





For this reason it is invalid to apply gradient to vector field.


You may either calculate sclalar product of gard and E(r),


denoted as div:





div E(r) = grad * E(r) = e_i e_k ∂E_k(r)/∂x_i = ∂E_i/∂x_i = 4πρ





or you can calculate vector product, denoted as rot:


rot B = grad x B(r) = Eijk ej ek ∂Bj/∂xi = 2πJ