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Find d/dx of x^(sin x) for x > 0 using logarithms.
Ax^(sin x) (cos x + sin x / x)
Bx^(sin x) (cos x ln x + 1/x)
Cx^(sin x) (cos x ln x - sin x / x)
Dx^(sin x) (cos x ln x + sin x / x)
Answer & Solution
Correct answer: D. x^(sin x) (cos x ln x + sin x / x)
Taking logs, ln y = sin x ln x, so y'/y = cos x ln x + sin x / x.
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