Apply your rule to gx ln xx does your answer agree with

Question

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).