Derivative of f(x)=-3x^8+2x^5+10x^3-3

1. Differentiate $- 3 x^{8} + 2 x^{5} + 10 x^{3} - 3$ 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: $x^{8}$ goes to $8 x^{7}$

      So, the result is: $- 24 x^{7}$

   2. 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: $10 x^{4}$

   3. 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: $30 x^{2}$

   4. The derivative of the constant $\left(-1\right) 3$ is zero.

   The result is: $- 24 x^{7} + 10 x^{4} + 30 x^{2}$

2. Now simplify:

   $$x^{2} \left(- 24 x^{5} + 10 x^{2} + 30\right)$$

The answer is:

$$x^{2} \left(- 24 x^{5} + 10 x^{2} + 30\right)$$