Derivative of 4sinx-6x+7

1. Differentiate $\left(- 6 x + 4 \sin{\left(x \right)}\right) + 7$ term by term:

   1. Differentiate $- 6 x + 4 \sin{\left(x \right)}$ 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 sine is cosine:

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

         So, the result is: $4 \cos{\left(x \right)}$

      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: $-6$

      The result is: $4 \cos{\left(x \right)} - 6$

   2. The derivative of the constant $7$ is zero.

   The result is: $4 \cos{\left(x \right)} - 6$

The answer is:

$$4 \cos{\left(x \right)} - 6$$