1. The function provided is f(x) = 5x + 7
2. To find the derivative of the function, apply the power rule for differentiation, which states that \frac{d}{dx}[ax^n] = nax^{n-1}
3. Thus, the derivative for the linear function (where n = 1 ) 5x is simply the coefficient of x
4. The derivative of a constant is zero, so the term 7 disappears when differentiated.
Answer: (f(x))' = 5