Let ( f(x) = x³(x - 9)⁵(x² - 2)⁴ ). Use logarithmic differentiation to determine the derivative ( f'(x) ).
a. ( f'(x) = 9x²(x - 9)⁵(x² - 2)⁴ + 5x³(x - 9)⁴(x² - 2)⁴ + 4x³(x - 9)⁵(x² - 2)³/x³(x - 9)⁵(x² - 2)⁴ )
b. ( f'(x) = 3x²(x - 9)⁵(x² - 2)⁴ + 5x³(x - 9)⁴(x² - 2)⁴ + 4x³(x - 9)⁵(x² - 2)³/x³(x - 9)⁵(x² - 2)⁴ )
c. ( f'(x) = 9x²(x - 9)⁴(x² - 2)⁵ + 5x³(x - 9)⁵(x² - 2)⁴ + 4x³(x - 9)⁵(x² - 2)³/x³(x - 9)⁵(x² - 2)⁴ )
d. ( f'(x) = 9x²(x - 9)⁵(x² - 2)⁴ + 5x³(x - 9)⁵(x² - 2)⁴ + 4x⁴(x - 9)⁵(x² - 2)³/x³(x - 9)⁵(x² - 2)⁴ )