Derivative of f(x)=7+3x-4x^2

1. Differentiate $- 4 x^{2} + \left(3 x + 7\right)$ term by term:

   1. Differentiate $3 x + 7$ term by term:

      1. The derivative of the constant $7$ is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $3$

      The result is: $3$

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x^{2}$ goes to $2 x$

      So, the result is: $- 8 x$

   The result is: $3 - 8 x$

The answer is:

$$3 - 8 x$$