Derivative of 5x^6-2x-4.5

1. Differentiate $\left(5 x^{6} - 2 x\right) - \frac{9}{2}$ term by term:

   1. Differentiate $5 x^{6} - 2 x$ 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: $x^{6}$ goes to $6 x^{5}$

         So, the result is: $30 x^{5}$

      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: $30 x^{5} - 2$

   2. The derivative of the constant $- \frac{9}{2}$ is zero.

   The result is: $30 x^{5} - 2$

The answer is:

$$30 x^{5} - 2$$