Derivative of 4*(x-2)^2-5

1. Differentiate $4 \left(x - 2\right)^{2} - 5$ term by term:

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

      1. Let $u = x - 2$.

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

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 2\right)$:

         1. Differentiate $x - 2$ term by term:

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

            2. The derivative of the constant $-2$ is zero.

            The result is: $1$

         The result of the chain rule is:

         $$2 x - 4$$

      So, the result is: $8 x - 16$

   2. The derivative of the constant $-5$ is zero.

   The result is: $8 x - 16$

The answer is: