Is the gradient of a function basically it's derivative?
For instance, given f(x) = 3x^4 + 6x^2 + 7x + 3, the gradient of f(x) would be f'(x) = 12x^3 + 12x + 7, right?
The gradient of a (scalar) field is a vector field. Suppose you have a scalar field, such as a temperature field . Then you can form a vector field called the gradient of phi.
So it is not the derivative but it is deeply related