Question: (a) Use a computer algebra system to differentiate (x + 1)x and (sin x)x.
(b) Conjecture a rule for differentiating (f(x))x, where f is any differentiable function.
(c) Apply your rule to g(x) = (ln x)x. Does your answer agree with the answer given by the computer algebra system?
(d) Prove your conjecture by rewriting (f(x))x in the form eh(x).