Derivative of f(x)=3^7-6x^5-4x^2+17

1. Differentiate $\left(- 4 x^{2} + \left(2187 - 6 x^{5}\right)\right) + 17$ term by term:

   1. Differentiate $- 4 x^{2} + \left(2187 - 6 x^{5}\right)$ term by term:

      1. Differentiate $2187 - 6 x^{5}$ term by term:

         1. The derivative of the constant $2187$ is zero.

         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: $- 30 x^{4}$

         The result is: $- 30 x^{4}$

      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: $- 8 x$

      The result is: $- 30 x^{4} - 8 x$

   2. The derivative of the constant $17$ is zero.

   The result is: $- 30 x^{4} - 8 x$

The answer is:

$$- 30 x^{4} - 8 x$$