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

1. Differentiate $5 x + \left(4 x^{3} - 5 x^{2}\right)$ term by term:

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

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

      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: $- 10 x$

      The result is: $12 x^{2} - 10 x$

   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: $12 x^{2} - 10 x + 5$

The answer is:

$$12 x^{2} - 10 x + 5$$