Derivative of 6(3x-sin(3x))

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

   1. Differentiate $3 x - \sin{\left(3 x \right)}$ 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: $x$ goes to $1$

         So, the result is: $3$

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

         1. Let $u = 3 x$.

         2. The derivative of sine is cosine:

            $$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$$

         3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x$:

            1. 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 of the chain rule is:

            $$3 \cos{\left(3 x \right)}$$

         So, the result is: $- 3 \cos{\left(3 x \right)}$

      The result is: $3 - 3 \cos{\left(3 x \right)}$

   So, the result is: $18 - 18 \cos{\left(3 x \right)}$

The answer is:

$$18 - 18 \cos{\left(3 x \right)}$$