Derivative of y=-10x+3cosx

1. Differentiate $- 10 x + 3 \cos{\left(x \right)}$ term by term:

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

      1. Apply the power rule: $x$ goes to $1$

      So, the result is: $-10$

   2. 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: $- 3 \sin{\left(x \right)}$

   The result is: $- 3 \sin{\left(x \right)} - 10$

The answer is:

$$- 3 \sin{\left(x \right)} - 10$$