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

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

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

   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: $15 x^{2}$

      So, the result is: $- 15 x^{2}$

   3. 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: $8 x$

   4. The derivative of the constant $\left(-1\right) 3$ is zero.

   The result is: $4 x^{3} - 15 x^{2} + 8 x$

2. Now simplify:

   $$x \left(4 x^{2} - 15 x + 8\right)$$

The answer is:

$$x \left(4 x^{2} - 15 x + 8\right)$$