Derivative of 3*(2-x)^6

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

   1. Let $u = 2 - x$.

   2. Apply the power rule: $u^{6}$ goes to $6 u^{5}$

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

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

         1. The derivative of the constant $2$ 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: $-1$

         The result is: $-1$

      The result of the chain rule is:

      $$- 6 \left(2 - x\right)^{5}$$

   So, the result is: $- 18 \left(2 - x\right)^{5}$

2. Now simplify:

   $$18 \left(x - 2\right)^{5}$$

The answer is:

$$18 \left(x - 2\right)^{5}$$