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

1. Differentiate $\left(2 x^{3} - 4 x^{2}\right) + 5$ term by term:

   1. Differentiate $2 x^{3} - 4 x^{2}$ 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. Apply the power rule: $x^{2}$ goes to $2 x$

         So, the result is: $- 8 x$

      The result is: $6 x^{2} - 8 x$

   2. The derivative of the constant $5$ is zero.

   The result is: $6 x^{2} - 8 x$

2. Now simplify:

   $$2 x \left(3 x - 4\right)$$

The answer is:

$$2 x \left(3 x - 4\right)$$