Derivative of 2x^3-9x^2-60x+1

1. Differentiate $2 x^{3} - 9 x^{2} - 60 x + 1$ 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: $6 x^{2}$

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

      1. 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: $18 x$

      So, the result is: $- 18 x$

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

      1. 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: $60$

      So, the result is: $-60$

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

   The result is: $6 x^{2} - 18 x - 60$

The answer is:

$$6 x^{2} - 18 x - 60$$