Derivative of 9x-cosx+10

1. Differentiate $\left(9 x - \cos{\left(x \right)}\right) + 10$ term by term:

   1. Differentiate $9 x - \cos{\left(x \right)}$ 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: $9$

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

      The result is: $\sin{\left(x \right)} + 9$

   2. The derivative of the constant $10$ is zero.

   The result is: $\sin{\left(x \right)} + 9$

The answer is:

$$\sin{\left(x \right)} + 9$$