Derivative of sin(x-(3/5))-(8/5)

1. Differentiate $\sin{\left(x - \frac{3}{5} \right)} - \frac{8}{5}$ term by term:

   1. Let $u = x - \frac{3}{5}$.

   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 $\frac{d}{d x} \left(x - \frac{3}{5}\right)$:

      1. Differentiate $x - \frac{3}{5}$ term by term:

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

         2. The derivative of the constant $- \frac{3}{5}$ is zero.

         The result is: $1$

      The result of the chain rule is:

      $$\cos{\left(x - \frac{3}{5} \right)}$$

   4. The derivative of the constant $- \frac{8}{5}$ is zero.

   The result is: $\cos{\left(x - \frac{3}{5} \right)}$

2. Now simplify:

   $$\cos{\left(x - \frac{3}{5} \right)}$$

The answer is:

$$\cos{\left(x - \frac{3}{5} \right)}$$