Derivative of sin(3*x-pi/12)

1. Let $u = 3 x - \frac{\pi}{12}$.

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 $\frac{d}{d x} \left(3 x - \frac{\pi}{12}\right)$:

   1. Differentiate $3 x - \frac{\pi}{12}$ 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 the constant $- \frac{\pi}{12}$ is zero.

      The result is: $3$

   The result of the chain rule is:

   $$3 \cos{\left(3 x - \frac{\pi}{12} \right)}$$

4. Now simplify:

   $$3 \sin{\left(3 x + \frac{5 \pi}{12} \right)}$$

The answer is: