3.5. DERIVATIVES OF PERIODIC FUNCTIONS 55 Focus on Theory: Establishing Derivative Formulas Example 3.24. Confirm that the derivative of g(x) = 3x2 is g'(x) = 6: by using the definition of the derivative. Example 3.25. Give an informal justification that the derivative of f (x) = e is f'(x) = ed by using the definition of the derivative. Example 3.26. Use the definition of the derivative to show that if f(x) = b + mr, for constants m and b, then f'(I) = m