Derivative of ax^2+bx+c

1. Differentiate $a x^{2} + b x + c$ 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: $2 a x$

   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: $b$

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

   The result is: $2 a x + b$

The answer is:

$$2 a x + b$$