Derivative of picos(pix/6)

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

   1. Let $u = \frac{\pi x}{6}$.

   2. The derivative of cosine is negative sine:

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{\pi x}{6}$:

      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: $\frac{\pi}{6}$

      The result of the chain rule is:

      $$- \frac{\pi \sin{\left(\frac{\pi x}{6} \right)}}{6}$$

   So, the result is: $- \frac{\pi^{2} \sin{\left(\frac{\pi x}{6} \right)}}{6}$

The answer is:

$$- \frac{\pi^{2} \sin{\left(\frac{\pi x}{6} \right)}}{6}$$