Derivative of f(x)=2x⁵-3x²

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

      So, the result is: $10 x^{4}$

   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: $- 6 x$

   The result is: $10 x^{4} - 6 x$

The answer is:

$$10 x^{4} - 6 x$$