Derivative of f(x)=3x^5-4x-10

1. Differentiate $\left(3 x^{5} - 4 x\right) - 10$ term by term:

   1. Differentiate $3 x^{5} - 4 x$ 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: $x^{5}$ goes to $5 x^{4}$

         So, the result is: $15 x^{4}$

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

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $-4$

      The result is: $15 x^{4} - 4$

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

   The result is: $15 x^{4} - 4$

The answer is:

$$15 x^{4} - 4$$