Derivative of (4x^2+3x+5)

1. Differentiate $4 x^{2} + 3 x + 5$ term by term:

   1. 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: $8 x$

   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: $3$

   3. The derivative of the constant $5$ is zero.

   The result is: $8 x + 3$

The answer is:

$$8 x + 3$$