Derivative of 3x^3-7x^2+2x-10

1. Differentiate $\left(2 x + \left(3 x^{3} - 7 x^{2}\right)\right) - 10$ term by term:

   1. Differentiate $2 x + \left(3 x^{3} - 7 x^{2}\right)$ term by term:

      1. Differentiate $3 x^{3} - 7 x^{2}$ 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: $x^{3}$ goes to $3 x^{2}$

            So, the result is: $9 x^{2}$

         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: $- 14 x$

         The result is: $9 x^{2} - 14 x$

      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: $9 x^{2} - 14 x + 2$

   2. The derivative of the constant $-10$ is zero.

   The result is: $9 x^{2} - 14 x + 2$

The answer is:

$$9 x^{2} - 14 x + 2$$