The prime function of a mathematical expression is not a standard mathematical concept. If you are referring to the derivative of the function f(x) = 3x² + 4, then that would be the function f'(x), which represents the rate of change of the original function with respect to the variable x.
To find the derivative of f(x) = 3x² + 4 with respect to x, you can use the power rule for differentiation. The power rule states that if you have a term of the form ax^n, the derivative with respect to x is n * ax^(n-1).
In this case, the derivative of f(x) = 3x² + 4 with respect to x is:
f'(x) = d/dx (3x² + 4) = 2 * 3x^(2-1) + 0 = 6x.
So, the derivative of f(x) is f'(x) = 6x. This is the prime function (derivative) of the given function f(x).