Derivative of -x^5+2*x^3-3*x^2-1

1. Differentiate $\left(- 3 x^{2} + \left(- x^{5} + 2 x^{3}\right)\right) - 1$ term by term:

   1. Differentiate $- 3 x^{2} + \left(- x^{5} + 2 x^{3}\right)$ term by term:

      1. Differentiate $- x^{5} + 2 x^{3}$ 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: $x^{5}$ goes to $5 x^{4}$

            So, the result is: $- 5 x^{4}$

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

            1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

            So, the result is: $6 x^{2}$

         The result is: $- 5 x^{4} + 6 x^{2}$

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

         1. Apply the power rule: $x^{2}$ goes to $2 x$

         So, the result is: $- 6 x$

      The result is: $- 5 x^{4} + 6 x^{2} - 6 x$

   2. The derivative of the constant $-1$ is zero.

   The result is: $- 5 x^{4} + 6 x^{2} - 6 x$

2. Now simplify:

   $$x \left(- 5 x^{3} + 6 x - 6\right)$$

The answer is:

$$x \left(- 5 x^{3} + 6 x - 6\right)$$