Derivative of -47x^10+-24x^9+10x^8-25x^7+37x^6+663

1. Differentiate $- 47 x^{10} - 24 x^{9} + 10 x^{8} - 25 x^{7} + 37 x^{6} + 663$ 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: $x^{10}$ goes to $10 x^{9}$

      So, the result is: $- 470 x^{9}$

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

      1. Apply the power rule: $x^{9}$ goes to $9 x^{8}$

      So, the result is: $- 216 x^{8}$

   3. 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: $80 x^{7}$

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

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

         1. Apply the power rule: $x^{7}$ goes to $7 x^{6}$

         So, the result is: $175 x^{6}$

      So, the result is: $- 175 x^{6}$

   5. 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: $222 x^{5}$

   6. The derivative of the constant $663$ is zero.

   The result is: $- 470 x^{9} - 216 x^{8} + 80 x^{7} - 175 x^{6} + 222 x^{5}$

2. Now simplify:

   $$x^{5} \left(- 470 x^{4} - 216 x^{3} + 80 x^{2} - 175 x + 222\right)$$

The answer is:

$$x^{5} \left(- 470 x^{4} - 216 x^{3} + 80 x^{2} - 175 x + 222\right)$$