Derivative of 2x^3-3x^2+4x-5

1. Differentiate $2 x^{3} - 3 x^{2} + 4 x - 5$ 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: $6 x$

      So, the result is: $- 6 x$

   3. 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: $4$

   4. The derivative of the constant $\left(-1\right) 5$ is zero.

   The result is: $6 x^{2} - 6 x + 4$

The answer is:

$$6 x^{2} - 6 x + 4$$