The limit definition of the derivative of f at x = a is given by lim(h→0) [f(a+h) - f(a)]/h. If f(x) = 5x³ - 2x, which of the following expressions is equivalent to f'(x)?

Core Concept

Using the power rule and constant multiple rule: d/dx[5x³] = 15x² and d/dx[-2x] = -2. By the sum/difference rule, f'(x) = 15x² - 2. This can be verified using the limit definition.