Derivative of y=x²-4x³+5

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

   1. Apply the power rule: $x^{2}$ goes to $2 x$

   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: $x^{3}$ goes to $3 x^{2}$

         So, the result is: $12 x^{2}$

      So, the result is: $- 12 x^{2}$

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

   The result is: $- 12 x^{2} + 2 x$

2. Now simplify:

   $$2 x \left(1 - 6 x\right)$$

The answer is:

$$2 x \left(1 - 6 x\right)$$