导数 (3x^7-15x^4+60x^2+120)'

1. Differentiate $\left(60 x^{2} + \left(3 x^{7} - 15 x^{4}\right)\right) + 120$ term by term:

   1. Differentiate $60 x^{2} + \left(3 x^{7} - 15 x^{4}\right)$ term by term:

      1. Differentiate $3 x^{7} - 15 x^{4}$ 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: $x^{7}$ goes to $7 x^{6}$

            So, the result is: $21 x^{6}$

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

            1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$

            So, the result is: $- 60 x^{3}$

         The result is: $21 x^{6} - 60 x^{3}$

      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: $120 x$

      The result is: $21 x^{6} - 60 x^{3} + 120 x$

   2. The derivative of the constant $120$ is zero.

   The result is: $21 x^{6} - 60 x^{3} + 120 x$

The answer is:

$$21 x^{6} - 60 x^{3} + 120 x$$