Derivative of x^6-6x^10+12x

1. Differentiate $12 x + \left(- 6 x^{10} + x^{6}\right)$ term by term:

   1. Differentiate $- 6 x^{10} + x^{6}$ term by term:

      1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$

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

         1. Apply the power rule: $x^{10}$ goes to $10 x^{9}$

         So, the result is: $- 60 x^{9}$

      The result is: $- 60 x^{9} + 6 x^{5}$

   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: $12$

   The result is: $- 60 x^{9} + 6 x^{5} + 12$

The answer is:

$$- 60 x^{9} + 6 x^{5} + 12$$