Derivative of f(x)=x⁵-4x³+2x-3

1. Differentiate $x^{5} - 4 x^{3} + 2 x - 3$ term by term:

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

   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: $x^{3}$ goes to $3 x^{2}$

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

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

   3. 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: $2$

   4. The derivative of the constant $\left(-1\right) 3$ is zero.

   The result is: $5 x^{4} - 12 x^{2} + 2$

The answer is:

$$5 x^{4} - 12 x^{2} + 2$$