Derivative of 3*cosx+7x

1. Differentiate $7 x + 3 \cos{\left(x \right)}$ term by term:

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

      1. The derivative of cosine is negative sine:

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

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

   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: $7$

   The result is: $7 - 3 \sin{\left(x \right)}$

The answer is:

$$7 - 3 \sin{\left(x \right)}$$