Derivative of f(x)=5x²-3x+2

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

      So, the result is: $10 x$

   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: $x$ goes to $1$

         So, the result is: $3$

      So, the result is: $-3$

   3. The derivative of the constant $2$ is zero.

   The result is: $10 x - 3$

The answer is:

$$10 x - 3$$