Derivative of 5*x^4-7*x^2-x

1. Differentiate $- x + \left(5 x^{4} - 7 x^{2}\right)$ term by term:

   1. Differentiate $5 x^{4} - 7 x^{2}$ 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: $x^{4}$ goes to $4 x^{3}$

         So, the result is: $20 x^{3}$

      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: $- 14 x$

      The result is: $20 x^{3} - 14 x$

   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: $-1$

   The result is: $20 x^{3} - 14 x - 1$

The answer is:

$$20 x^{3} - 14 x - 1$$