(a) Use a computer algebra system to differentiate (x + 1)x and (sin x) x. (b)

Chapter 0, Problem 123

(choose chapter or problem)

(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) .

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