Determine whether the following statements are true and give an explanation or counterexample.

a. The derivative of log₂ 9 = 1/(9 ln 2).

b. ln (x + 1) + ln (x - 1) = ln (x² - 1), for all x.

c. The exponential function 2^{x + 1} can be written in base e as e^{2 ln (x + 1)}.

d. d/dx (√2^x) = x√2^{x - 1}.

e. d/dx (x^√2) = √2 x^{√2 - 1}.