Derivative of x^4-6x^2+5x

1. Differentiate $5 x + \left(x^{4} - 6 x^{2}\right)$ term by term:

   1. Differentiate $x^{4} - 6 x^{2}$ 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. Apply the power rule: $x^{2}$ goes to $2 x$

         So, the result is: $- 12 x$

      The result is: $4 x^{3} - 12 x$

   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: $5$

   The result is: $4 x^{3} - 12 x + 5$

The answer is:

$$4 x^{3} - 12 x + 5$$