Derivative of y=5-4x+7x³-x^5

1. Differentiate $- x^{5} + \left(7 x^{3} + \left(5 - 4 x\right)\right)$ term by term:

   1. Differentiate $7 x^{3} + \left(5 - 4 x\right)$ term by term:

      1. Differentiate $5 - 4 x$ term by term:

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

         2. 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: $-4$

         The result is: $-4$

      2. 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: $21 x^{2}$

      The result is: $21 x^{2} - 4$

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

      1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$

      So, the result is: $- 5 x^{4}$

   The result is: $- 5 x^{4} + 21 x^{2} - 4$

The answer is:

$$- 5 x^{4} + 21 x^{2} - 4$$