Derivative of 6cos(7x+(pi))

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

   1. Let $u = 7 x + \pi$.

   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 $\frac{d}{d x} \left(7 x + \pi\right)$:

      1. Differentiate $7 x + \pi$ 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: $7$

         2. The derivative of the constant $\pi$ is zero.

         The result is: $7$

      The result of the chain rule is:

      $$7 \sin{\left(7 x \right)}$$

   So, the result is: $42 \sin{\left(7 x \right)}$

The answer is:

$$42 \sin{\left(7 x \right)}$$