Derivative of (3-((5*pi)/4)+(5*x)-(5*sqrt(2)*sinx))

1. Differentiate $\left(5 x + \left(- \frac{5 \pi}{4} + 3\right)\right) - 5 \sqrt{2} \sin{\left(x \right)}$ term by term:

   1. Differentiate $5 x + \left(- \frac{5 \pi}{4} + 3\right)$ term by term:

      1. The derivative of the constant $- \frac{5 \pi}{4} + 3$ 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: $5$

      The result is: $5$

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

   The result is: $- 5 \sqrt{2} \cos{\left(x \right)} + 5$

The answer is:

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