Derivative of (sin(5-2x))/-2

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

   1. Let $u = 5 - 2 x$.

   2. The derivative of sine is cosine:

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(5 - 2 x\right)$:

      1. Differentiate $5 - 2 x$ term by term:

         1. The derivative of the constant $5$ is zero.

         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: $-2$

         The result is: $-2$

      The result of the chain rule is:

      $$- 2 \cos{\left(2 x - 5 \right)}$$

   So, the result is: $\cos{\left(2 x - 5 \right)}$

The answer is:

$$\cos{\left(2 x - 5 \right)}$$